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ECON20110 Fall 2013 - Lecture 17: Democracy Squared — Transcript

by Glen Weyl · 11,957 words · 2,076 segments · language en · Watch on YouTube

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0:03okay so this is the last uh lecture
0:06um
0:08and
0:10most of the class
0:12uh so far has covered sort of broad
0:14topics but for the last class i want to
0:17talk to you about a more specific
0:18proposal
0:21um which hopefully will give you a sense
0:24of economics in action
0:26in particular we'll talk about yeah
0:29oh crap
0:48um
0:50in particular this is an alternative to
0:52democracy that i've proposed in my uh
0:55work
0:56and we're going to start by giving a
0:58little background
0:59uh on
1:01the impossible classic impossibility
1:05results showing
1:06uh even more clearly the problems with
1:08voting that we started developing the
1:10previous
1:12class i'll then talk about some of the
1:14problems with previous economic
1:16alternatives to voting i'll then discuss
1:19my
1:20quadratic voting proposal give some
1:22basic intuition of why it works and why
1:24it takes the specific form it does
1:26i'll then talk a little bit about
1:28robustness and the breadth with which it
1:30can be used
1:31then i'll talk about some of the
1:32applications of it
1:34what i'm doing right now to try to make
1:36it a reality
1:39and
1:40uh
1:41use that as a way to show you
1:43sort of what economists can do the
1:45different roles they can play in
1:47bringing economic ideas uh to to
1:50practice and then i'll give a brief
1:52wrap-up of the course okay
1:55so we talked about the problems with
1:57voting uh in the previous class
2:00but these get much worse when there are
2:02multiple alternatives and this was a
2:05problem that was first
2:09discussed by the marquis de condorcet
2:11in 1785
2:13and he gave an example imagine that
2:15there's three candidates a b and c and
2:18three voters the first voter prefers a
2:21and then their second choice is b
2:23and then their third choice is c
2:25the second voter prefers b and their
2:27second choice is c and their third
2:29choice is a
2:31and the third voter prefers c and then
2:33their second choice is a and their third
2:35choices b
2:37now uh maury uh who would you consider
2:40the winner in this election like who do
2:42you think is a reasonable person to
2:43choose out because you win say that any
2:46of them are any options or winners
3:03um you know a beats b right because one
3:06and yeah and then
3:09a b to b
3:10b
3:11c but c b a yes so so can you just
3:14explain that a little more so everybody
3:16else gets it yeah so
3:18i guess if you know that a is better
3:20than b if b is better than c then a
3:24should be better than c yeah
3:26but if you compare it there you can tell
3:27that c is better than a
3:29yeah because there are two people who
3:31would vote for c over a yeah two people
3:33would vote for b over c and two people
3:35would go for a over b right
3:38um
3:40and so there doesn't really seem to be a
3:42good reason to favor one and this is
3:44called condorcet's paradox of voting now
3:46one way you could interpret this is that
3:48this is just a tie among candidates and
3:50perhaps there's some uh coherent system
3:54uh that could
3:56you know
3:57uh give you something and many systems
4:01have been proposed in practice like
4:03runoffs plurality rules etc
4:06but
4:07in 1950
4:09kenneth arrow showed that there was a
4:11fundam there are fundamental limits on
4:13any system where we only receive from
4:16individuals the order of preferences
4:18that they have
4:19and to do that he proposed some basic
4:21principles that any
4:24system should try to satisfy
4:28uh in christian
4:30question
4:31um
4:32what were the principles that arrow
4:34thought that any voting system should
4:35try to satisfy uh one is pareto
4:38efficiency
4:40yeah okay
4:42so basically that if one one person
4:44can't be made better off without harming
4:46another person yeah um another point is
4:49i think
4:50independence of alternatives have
4:51irrelevant alternatives yeah relevant
4:53alternatives so you can't like be voting
4:55a versus b and then someone wants to
4:58input in an option c
5:00that would sway the election yep that's
5:03right um
5:10third one is that any preference
5:11ordering has to be admissible like you
5:13can't restrict people from saying
5:15certain preferences or disorders yeah so
5:17independent of a relevant alternative
5:19says that um if
5:23we're thinking about whether a is
5:25beating b or not the introduction of
5:27another option
5:28c can't change whether a beats
5:31b
5:33um
5:34okay so that leads to uh
5:39this result which is called arrows
5:40general possibility theorem which says
5:43that the only social choice rule
5:45satisfying these three principles
5:47is dictatorship
5:49that is that one individual always
5:51determines
5:52who wins regardless of what anyone else
5:54says
5:56and this provides a pretty strong sense
5:58in which democracy is flawed there's no
6:00non-dictatorial system that obeys all of
6:03these three principles
6:05and you know maybe
6:06a system like having a runoff or
6:10other systems that you might think of
6:12could work better in some sense than
6:14others but they're all in some sense
6:16going to run into this fundamental
6:17incoherence at some point
6:21and
6:22some responded to this by saying that
6:25independence
6:26of irrelevant alternatives was too
6:29strong of a condition
6:31that
6:32perhaps when we introduce uh
6:34you know option c
6:37that um some people
6:40will rank c very highly and maybe that
6:43means that they really like c and they
6:46didn't care that much about a and b and
6:47maybe we should take that into account
6:50in determining
6:53how much weight their votes have and
6:55therefore maybe it could change
6:58a versus b
6:59but
7:00gibbert and satirthwaite
7:02uh
7:04proved that any system that didn't
7:05satisfy your independence of your
7:07relevant alternatives would sometimes
7:09give people an incentive to lie about
7:11their preferences
7:12and the reason is
7:14um
7:16that well okay so um
7:19uh tavish can you explain why if a
7:22system doesn't satisfy independence of
7:24your relevant alternatives it would give
7:25you an incentive sometimes to lie about
7:27your preferences
7:36do you have an incentive
7:40which all right that doesn't satisfy
7:42independent of irrelevant alternatives
7:44why would it give you an incentive to
7:45lie about your preferences in some
7:47occasions
7:56if you didn't like neither of them
7:58matter to you or
8:00your
8:02side off
8:03so okay so imagine that the voting
8:05system that we have does not satisfy
8:07independence for relevant alternatives
8:09that is for example sometimes
8:11we might use the fact that you rate
8:14c as your top choice to inform
8:18whether a versus b wins
8:21the election why would that give you an
8:23incentive to lie about your preferences
8:26um
8:27if if you do care about averse's b
8:29rather than this even
8:31would it so that would
8:33encourage you to
8:34vote in favor of c um
8:37you know c is
8:40yeah so you're you're getting in the
8:42right direction so imagine that we have
8:44an election where we know that a and b
8:46are going to be like the most likely
8:48ones to win
8:49but now we use the fact that you rank c
8:51first to like downgrade how much weight
8:53we put on how you rate a versus b
8:58then
8:59that's going to give you an incentive
9:02when you know that a and b are the only
9:03two realistic ones that could win
9:06to not rate c first even though c is
9:08your favorite
9:10um
9:11okay so arrow's result remains true if
9:15we replace iia with strategy-proofness
9:18which is that no matter what anyone else
9:19does you always have an incentive to
9:21report truthfully
9:23so this is all
9:25pretty pessimistic right but it relies
9:29on some very strong assumptions
9:31strategy proofness
9:33is a very strong assumption it says that
9:35you never have an incentive to lie at
9:37all regardless of anyone else says
9:40and at least as importantly
9:43the these systems
9:45require that people
9:47report only their ordinal preferences
9:50only this is my favorite this is my
9:52second favorite this is my third
9:54favorite and not how strongly they feel
9:56about different things right
10:00and
10:01in some sense i think that you only
10:03reporting your cardinal preference
10:05ordinal preferences is sort of a
10:07fundamental feature of democracy it says
10:09that everyone gets sort of the same
10:11amount of vote
10:12right it's like one man one vote
10:15but
10:15it's sort of a basic limitation of
10:17democracy as well and a lot of this
10:19class is going to be about how by
10:21relaxing the notion
10:23that you only get one person one vote
10:26you can um
10:29you can
10:30do better okay
10:33so
10:34um
10:35a natural approach
10:37that incorporates cardinality that
10:39incorporates how strongly you feel about
10:40issues is the vcg mechanism
10:44so imagine we're choosing between two
10:46alternatives a and b
10:48everyone can say how much they prefer
10:50alternative a versus b or b versus a
10:54and um
10:56the
10:57if you cause as a result of your report
11:00the total to switch from being in favor
11:03of a to being in favor of b then you
11:05have to then you have to pay the total
11:08amount by which people other than you
11:10preferred a
11:12or vice versa if you caused it to switch
11:15from b to a then you have to pay the
11:17total amount by which other people
11:19preferred
11:20b
11:22um
11:24and
11:25unfortunately though
11:27some of the problems that arise in vcg
11:30which i mentioned i think a little bit
11:32in class are particularly severe uh in
11:35this context
11:37okay so one thing that we talked about
11:39with vcg
11:40is that any money that it raises
11:43has to be destroyed rather than refunded
11:45back to people involved right
11:47um
11:48because otherwise people have an
11:50incentive to exaggerate how strongly
11:53they feel about something just to force
11:54other people to pay more
11:56right
11:57and that could be a pretty big problem
11:59here because this is a big collective
12:01decision taken among a large number of
12:03people what are you going to do with the
12:04money you can't give it to anyone you've
12:05just got to destroy it
12:07the second and probably more severe
12:10problem is collusion
12:12so
12:13if any two individuals
12:15report an overwhelming preference for a
12:18over b
12:19then
12:20each one of them individually would have
12:22guaranteed that a wins and that would in
12:25turn guarantee that neither of them have
12:28to make any payments
12:30why is that because once a is winning
12:34then they're not pivotal they're not
12:35changing the decision and therefore uh
12:38they don't have to make any payments yep
12:40all right um
12:41suppose there was like a lot of people
12:44and
12:46so like everybody would have an
12:47incentive to do that right so wouldn't
12:49that like kind of offset it in some
12:52sense well i mean it would sort of turn
12:53into chaos right like i don't know what
12:55the equilibrium would be at that point
12:57you know what i mean
12:59uh it might be something
13:01very crazy
13:03i mean i just don't know
13:05right
13:06no one's ever studied that as far as i
13:08know
13:10um
13:11so what that means is this system is
13:13like incredibly incredibly incredibly
13:15sensitive to collusion so
13:17how varian the author of your textbook
13:19told me
13:20a story of when he was giving a class
13:22like this at michigan and trying to
13:24teach people about vcg he ran
13:27one of these things where they did the
13:28vcg mechanism to determine the date of
13:30the final exam
13:31and most people were like oh it's worth
13:33two dollars to me this day three dollars
13:35to me that day whatever
13:37and then one girl said oh it's worth a
13:39thousand dollars to me to have it on
13:41this day
13:42and then how was like really worth a
13:45thousand she's like oh yeah i have this
13:46incredible commitment it's worth a
13:47thousand dollars to me and then the next
13:49girl sitting next to her was her best
13:51friend said oh yeah it's worth a
13:52thousand dollars to me to heaven
13:55right
13:56and so obviously they'd figured out the
13:58collusive
14:00attack against vcg right so as a result
14:03of this most people think vcg is sort of
14:05hopelessly impractical
14:07um
14:09but
14:10one thing to notice remember when we
14:12looked at the vcg payments
14:14that you had to make
14:16um
14:18remember that
14:19if rather than being a binary decision
14:22it was one of these continuous decisions
14:24where we were saying how much of an
14:26externality to create
14:28when um if this is the cost to everyone
14:30else and this is the cost to you if we
14:32add those up
14:33the amount that you end up paying is
14:35this harberger triangle which is
14:37quadratic in the amount by which you
14:39shift the decision
14:42and that was the basis
14:44when i sort of realized that that was
14:46the basis
14:48for an alternative mechanism that we're
14:50going to spend most of today's class
14:52discussing
14:54um
14:55and this is called quadratic voting and
14:58with a binary decision it's uh
15:01it takes a very simple form
15:03uh philip what is the what is quadratic
15:06voting on a binary decision how does it
15:08well
15:09the
15:11the polar calls out like you may buy
15:15both positive or negative votes and your
15:19the number the cost of your votes is
15:21proportional the square of the number of
15:22votes to request and then it'll add up
15:25all the votes and implement the site
15:27that
15:28gets more yep and then the money gets
15:30refunded back to people so that the
15:32budget is balanced right
15:35so
15:36this basically by this logic here like
15:39vcg makes everyone pay their externality
15:41but it does so in a way
15:43that is much less
15:46complicated in some sense
15:49and which is
15:52sort of self-estimated
15:54rather than being estimated based on
15:56what everybody else says in much the
15:59same way that a first price auction
16:01you know you tried it you end up paying
16:03the amount that you sort of think the
16:05next guy is going to pay
16:07right because you're just trying just to
16:08beat him
16:10but you're doing that calculation rather
16:12than him telling the auctioneer what it
16:16will be and as a result of that it's not
16:18as subject to these collusive problems
16:20it also avoids the revenue problem you
16:22don't have to destroy the revenue you
16:23can give it back to people yeah phillip
16:26um how come that there is no severe
16:28problem with
16:30perverse incentives with the revenues in
16:33puerto rico
16:34because um what created the revenue
16:38incentive problem was the fact that what
16:41you say determines how much other people
16:43pay
16:44but here it's not it's what you say
16:47determines only what you pay
16:49and so that problem doesn't arise so the
16:51source of the collusion problem and of
16:53the revenue problem is the same it's
16:54that other people are determining what
16:56each other each person pays yeah mike um
16:59i have a question about the refunding
17:01yeah
17:02if you have like a quadratic vote over a
17:04bunch of outcomes yeah um
17:07is the redistribution only to the people
17:09who and then like one outcome wins but
17:11like a few people voted for that one
17:12yeah is the redistribution to everybody
17:14or just like the people besides the
17:16person who cast the highest vote or to
17:18everybody who didn't vote for that
17:19outcome it it can it's in any
17:22redistribution is done in any way
17:24such that everyone gets back the same
17:26fraction of the money they themselves
17:28put in so there's a million different
17:30ways that would have that would have
17:33that so like one way i could do that is
17:35that uh tanner gets the money that you
17:38paid
17:39uh you know adam gets the money that
17:41tanner paid etc you know i could have a
17:43system like that i could have everybody
17:45get one over n of what everybody puts in
17:48i could have people get
17:51um some share of what everyone other
17:53than them puts in but then one over n of
17:56what they put in i mean there's like a
17:58million different ways we were talking
18:00about like a quadratic vote yeah with
18:03people from this past yesterday and yeah
18:05uh like if you're picking
18:07from a bunch of restaurants to go to
18:08yeah there's one that like everybody
18:10clearly hates and would not be picked
18:12then could somebody cast like a very
18:14small vote on that restaurant and then
18:16just like with the intention of getting
18:18money redistributed oh no whenever you
18:20take the vote it has to
18:21like they can't
18:23get back
18:25you have to pull all the money from the
18:27entire vote that you do together
18:29and then you have to redistribute that
18:32stuff back in a way so that people get a
18:34constant fraction of the total amount
18:36that they paid in but but you know one
18:38over n would would be fine okay yeah
18:41so um
18:42do you know how multi-option quadratic
18:44voting
18:45works
18:46that wasn't described as much in the
18:48paper
18:49was it we were just trying you're trying
18:51to figure it out
18:52well i'll talk about that a little bit
18:54later but just to answer the question
18:56now
18:57the way that it works is you choose one
18:59option to be the default option
19:01and then for all the options that are
19:03not the default option everyone's
19:05allowed to buy votes in favor of or
19:07against those options
19:09and then if all options have other than
19:12the default
19:13have negative votes the default wins
19:17and if any option has positive votes
19:19then whichever has most positive votes
19:25okay
19:26so um
19:28quadratic voting
19:30has many attractive features and i'll
19:31just give sort of a glimpse of this
19:33today i'll give some more intuition
19:35about why it works why quadratic exactly
19:38and then i'll talk about robustness
19:39along many dimensions like collusion as
19:41well as applications okay so i want to
19:44try to keep the math to a minimum in the
19:46this lecture so i'm just going to focus
19:48on intuitions
19:49let's let
19:50the utility that an individual gets in
19:53units of dollars from an outcome
19:56uh be ui
19:58which may be positive or negative
20:01uh they're either in favor of
20:02implementing the alternative to the
20:03status quo or negative if they're
20:06against
20:07and the other crucial quantity is the
20:10chance that one vote changes the outcome
20:14and the key idea is that in a large
20:17group of people
20:19this chance that one vote changes the
20:22outcome will not vary very much with the
20:24number of votes that you buy so the idea
20:27is that you know
20:28if you think about bush winning by 400
20:30votes or gore winning by 400 votes these
20:33were basically like the same events up
20:35to hanging chads right they were all
20:37like they vote the election is roughly
20:39tied
20:39right there's really no way to tell the
20:41difference between these different
20:42things
20:43and in this sense it's like a market
20:44price it's something that doesn't very
20:48much
20:49with the behavior of any individual
20:51person and that's why the mechanism
20:53works it works very much like a market
20:56only large individuals
20:59will have market power and cause
21:01problems
21:04and we're going to denote this number
21:06this chance of a tie the density of
21:08pivotality by p
21:10both because it's for pivotality
21:12and because it looks like a
21:14price so
21:17together this utility that you get and
21:20the chance that an additional vote
21:22determines
21:24changes the election outcome determines
21:25the marginal utility that you get from
21:28buying an additional vote can someone
21:30say what uh
21:32that is uh is wesley here yeah yeah
21:35wesley yeah yeah i think
21:40look up
21:42what
21:42what is the marginal utility that you
21:44get from buying an additional vote if p
21:47is the chance that that vote changes the
21:49election outcome and ui is the utility
21:51that you get
21:52from
21:53uh
21:54the election going one way or the other
21:56okay then i guess it would just be the
21:59product number two yeah it's p times u
22:01right
22:03um
22:05and what's the marginal cost of an
22:07additional vote kim
22:11this quote the price of votes is the
22:13square of the number of votes you buy so
22:14what's the marginal cost of the
22:18yeah exactly
22:20so dake can you tell us what the first
22:23order condition uh
22:25then is going to be
22:27for
22:28the optimal number of votes to buy um
22:30well then you would set the marginal
22:32cost of the vote to
22:34um the marginality total benefit of the
22:36yeah so you said 2vi to
22:39p
22:40times u i
22:42so then uh
22:44vi equals p over 2 times ui exactly
22:50so
22:51notice that this is efficiency why is
22:53this efficiency because everyone buys
22:54votes in proportion to how much they
22:56care about the issue
22:58so let me give just a numerical uh
23:00illustration so
23:03imagine that you're deciding whether to
23:04go out to dinner or using your dorm's
23:07budget
23:08and person x is 60 dollars in favor of
23:11doing this and person people y and z are
23:1520 and 10
23:17against it
23:18so imagine that the chance that one
23:20additional vote changes the outcome is
23:22one tenth
23:23uh
23:24wesley then what are going to be
23:27the um
23:30purchases of votes by each of these
23:31individuals
23:34all right and
23:37uh
23:38so
23:40p is one tenth so p over two is one or
23:42twenty yeah so perhaps you do three
23:44he'll buy three votes yeah yeah one by
23:47uh one
23:48and
23:51yep that's right
23:52though i actually got this wrong because
23:54i forgot to divide by two okay but uh
23:56so
23:58what do you buy yeah you can buy a
24:00continuous number of votes
24:02um
24:04okay
24:05uh
24:06and what are going to be
24:08the payments uh associated with that
24:11anybody
24:13uh there you see
24:15you're just uh squaring everything so
24:17yeah x plus three that's nine
24:19dollars yep 379 dollars and then uh
24:22one and a half become one dollar and uh
24:25four two five yeah
24:28uh yes this is wrong again um
24:31so then each of them is going to get
24:3510 25 divided by 3 equals
24:42roughly like
24:44350 or something like that back
24:47um
24:48and
24:50notice that um
24:54okay
24:55so i this isn't quite
24:58right in this case so um they get 350
25:02back
25:04uh so y and z are going to be worse off
25:07x is going to be better off but at least
25:09they get three dollars and 50 cents back
25:12to compensate them for the fact that
25:13they don't get
25:14things in the direction and if you
25:16scaled things slightly differently
25:19as i had done here if it had been a one
25:21in five chance for example
25:23then it actually would have been that
25:26y
25:27would have been
25:28worse off but z actually would have been
25:31equally well or sorry would have been
25:32better off
25:34uh than under democracy even though
25:36she loses because she gets the money
25:38back this is what philip was saying
25:39earlier about redistribution of the flex
25:41dollars to the people who value them the
25:43most right
25:45um
25:46so overall this is a social gain because
25:49the person who cared the most
25:51got it and the losers were compensated
25:53except for people who were losers uh and
25:56works relatively extreme because they
25:59make larger payments yeah tanner how do
26:01you calculate the uh
26:03pivot
26:04reality
26:05vitality chance yeah
26:07um well you have to figure out what the
26:10distribution of values that people could
26:11have is
26:12and then you'll like there's a
26:14computation that you basically do
26:16there's a formula that's in the paper
26:18that gives you like an approximation to
26:19what that will be
26:21um
26:23doesn't this still play back right back
26:25into the issue that uh mike brought up
26:27uh not too long ago yeah about
26:28compensation because uh theoretically if
26:31someone were to
26:32quote unquote buy into this decision
26:34with like a penny
26:36um but then they get compensated back
26:39yes you have to decide the set of people
26:40who are allowed to participate
26:42separately from
26:44like how much they're actually going to
26:45participate conditional on their
26:46participation okay so you have to like
26:48basically figure out like based on your
26:50ex sense like is everyone roughly equal
26:53are there some people who are like more
26:54important to this decision give them
26:56back a bigger share of the revenues that
26:59come back like in like a practical sense
27:01if you have like uh
27:03with companies in the paper that we
27:04wrote
27:05for today
27:06um the value since the value is returned
27:08like kind of indirectly through the
27:10shares yeah
27:11so then it's proportional to the shares
27:15uh yeah right um
27:17if
27:19if pivotality approaches zero as the
27:23number of people increases it does yeah
27:24doesn't that have the same sort of issue
27:26with like
27:27you don't have an incentive to vote
27:30that so that would be true you currently
27:32don't have an incentive to vote right
27:33now
27:35i'll talk a little bit later about like
27:39you know why people actually do vote
27:41and if people continue to
27:44vote more than the model suggests for
27:46those reasons that's actually fine as
27:48long as they sort of like up weight how
27:51much they vote by in proportion to their
27:53utility
27:54right
27:55that'll still lead to the same thing in
27:57fact it actually leads it to be more
27:58efficient it turns out so
28:01you are
28:02um so depending like what people know
28:04about everybody else even if it's a
28:05really large market yeah
28:07wouldn't like couldn't people have
28:09different pivotal
28:10fatalities
28:14so in a large market
28:16um under most conditions they won't
28:19under some conditions they will
28:21so
28:22uh we'll talk a lot about stuff like
28:25that but
28:26uh yeah i mean as the number of people
28:28gets large under most conditions
28:30it will converge to it being the same
28:32for everybody but there are some
28:34conditions under which it won't
28:36usually it's not very far off and so you
28:38get very close to full efficiency much
28:40closer than you do under voting but yeah
28:50yeah
28:51that's right
28:53um
28:56okay oh yeah so
29:00it was
29:01in practice it's pretty difficult for
29:03people to calculate those values at
29:05least from some of the experimental
29:07evidence right
29:09maybe or i mean
29:11in first price auctions people usually
29:13do a pretty good job guessing
29:15what like the next highest person is
29:16going to bid they behave
29:18not too far off from equilibrium the
29:20hope would be you could do something
29:21similar here but of course
29:24when you have like a really high stakes
29:26situation and people are really
29:28uncertain about what's going on you'd
29:29prefer to have some more like open
29:31option that helps people get a sense for
29:33what's going on and you could do that
29:34here as well because you could have
29:36everyone like reporting how much they
29:38value
29:39the thing and then the computer could
29:41estimate use as i was saying with tanner
29:43based on that what's the density of
29:45pivotality and then could tell people
29:47advice about what they should do and you
29:49could do rounds of that and it would be
29:51like an auction you would have like a
29:53posted like density of pivotality and
29:56like as people changed their values the
29:59computer would be constantly
30:00re-estimating the chance of being
30:02pivotal and so you could you could do a
30:04system like that
30:05oh yeah
30:06that would also uh involve people
30:08reporting self-reporting values would
30:10that be open wouldn't that be uh have
30:12the same problem well because not any
30:15one individual will have much of an it's
30:17similar like to running an auction right
30:19in an auction you could like bid wrongly
30:22to try to move the price but if there's
30:23a large number of people you can't move
30:25the price much by the way you bid and so
30:27you have
30:28more of an incentive to like just avoid
30:30getting caught on the wrong side of the
30:31price than you do to try to manipulate
30:33the price
30:35so
30:36um okay
30:38so you might ask why we use the
30:40quadratic rule in particular
30:43um
30:44and to think about this let's consider
30:47uh
30:48that the um
30:51let's consider an alternative rule where
30:53you pay this uh not the square of the
30:55number of votes you buy but the number
30:56of votes you buy to the power x and i'm
30:59being a little sloppy here because of
31:01course
31:01uh this can hide or not hide the sign
31:05depending on whether the power x is odd
31:07or even but what i really mean by this
31:10is you pay the absolute value of the
31:13number of o2 by to the power of x okay
31:16so then the marginal benefit you get
31:17from buying additional vote is still p
31:19times u but the cost is now
31:22x times v to the x minus one
31:25um and so then
31:27can somebody tell me what the
31:30density sorry what the optimal
31:32um number of votes for people to buy is
31:35going to be there
31:37all right yeah well you'd use the same
31:39method you set the marginal cost to the
31:41marginal but if it's
31:44equals x times e to the x minus one yeah
31:47um so to figure out what the x minus v
31:50is
31:51um you divide p u by x yeah so then you
31:54have p p over x times u
31:56and then u
31:58um uh power
32:00both sides by one over one minus
32:04one over x minus one yeah so ignoring
32:07the constants there everyone's gonna buy
32:08votes in proportion to u to the x one
32:11over x minus one power and that means
32:13the decision is not going to be based on
32:15the sum of people's utilities but the
32:17sum of their utilities to the power 1
32:19over x minus 1
32:21which is efficient if and only if x is
32:23equal to 2
32:25right if x is less than two you're going
32:27to put too much weight on the extremists
32:29the people with very strong opinions
32:31because you'll do a convex
32:33transformation of utility so people with
32:35very extreme utilities will get a higher
32:37weight than people with small utilities
32:40if x is greater than two you put too
32:42little weight on the extremes and
32:44therefore you reduce the amount that you
32:46care about the intensity of people's
32:47preferences
32:48um
32:50okay so in fact we can relate this to
32:53other forms of
32:55government by changing x right
32:59so as
33:01x approaches infinity
33:03everyone is going to buy exactly one
33:06vote why is that someone explain that
33:09yeah sure yeah the exponent one over x
33:11minus one is gonna go to zero yep so u
33:14zero is just one
33:16exactly so this goes to majority rules
33:19democracy
33:20right because ever it's one man one vote
33:22then
33:23on the other hand as x goes to one and
33:25we get towards linear vote buying what's
33:27going to happen
33:29uh yeah rishi question on the previous
33:31part
33:32question yeah as x goes to infinity
33:34wouldn't
33:34the value go to k
33:38yeah but i mean the point is it's equal
33:39number of votes i mean it doesn't matter
33:41what the number of votes people have
33:43said yeah
33:46um
33:48yeah dig
33:49oh yeah yeah yeah answer it yeah um well
33:52if x goes to one then it would just go
33:54to one over
33:56um
33:57one over one because well one over zero
33:58sorry yeah so then it would become
34:02that you do the value which means yeah
34:04that you would have an infinite amount
34:07of votes depending on people would just
34:09buy infinite amounts depending on well
34:12in particular the ratio between the
34:14number of votes bought by someone who is
34:16a slightly higher utility someone is a
34:18slightly lower would go to infinity
34:20and so that means that the person with
34:23the most intense preference
34:25would buy infinitely more than the
34:26person with even slightly less and
34:28therefore that you'll have dictatorship
34:30of the individual with the most intense
34:32preference
34:35and
34:38the reason intuitively for that is that
34:41when you have linear voting it's like an
34:43auction the person who's willing to pay
34:45the most will buy infinitely more votes
34:47than the person who's willing to pay
34:48even a little bit less so basically you
34:51auction off the country to the highest
34:54bidder
34:55yeah all right does that
34:57happen the bcg mechanism is well like if
35:00there's
35:02no because everyone there will buy as it
35:04has a unilateral incentive at least
35:06weekly to buy things exactly equal to
35:09how much they care and you add that
35:11assumption that everybody's colluding
35:13oh under the assumption that people are
35:14colluding that could
35:16well happen i mean i'm not completely
35:18sure i haven't thought through enough
35:19what the equilibrium when people glued
35:21it looks like there you have to specify
35:24exactly what you mean by what collusive
35:26groups form
35:27so
35:28um
35:30so in and systems in between
35:33can be thought of as intermediate values
35:35of x so like x if x equals one is
35:38dictatorship and x equals infinity is
35:40democracy oligarchy is sort of like x
35:43between one and two and republics are
35:45sort of like x between two and infinity
35:48and you know since aristotle's time
35:49we've been debating between you know the
35:53uh these different forms of government
35:55we didn't have some coherent spectrum on
35:57which to put them and therefore was hard
35:59to figure out sort of what the optimum
36:00was
36:01and i think this way of looking at
36:03things makes clear that the optimal
36:05point is when there's two
36:07and in fact in different parts of our
36:08political system we use different values
36:11of x effectively we have majority rules
36:13voting determining many things but we
36:15also have lobbying and you know campaign
36:18contributions and money in politics that
36:21essentially auctions things the highest
36:22bidder in some cases so they were using
36:24x closer to one
36:26but the optimum is in is in as many
36:29areas as possible to make x equal to two
36:32okay
36:33now of course um
36:36my main criticism of the vcg mechanism
36:39was that it was very sensitive to
36:41collusion and so a natural question
36:44is
36:44uh how sensitive
36:49qv
36:51is
36:52to collusion um
36:55and
36:56uh
36:58tavish can you think of a reason why
37:00people would want to collude in qv
37:08um
37:34a glitter powder
37:36what would be the benefit to them of
37:38colluding under qv
37:56for some purpose beyond just getting
37:58what they want
38:00well i mean like can they benefit from
38:02including is it collusion proof are
38:04there benefits to colluding um
38:08again i can't think of a specific way
38:11evan well it becomes cheaper
38:14how so
38:15well
38:16i mean so the way i'm thinking about it
38:18is is suppose you buy um
38:21k times two on votes yeah her spend that
38:23much dollars you get square root of that
38:26votes
38:27square root of k times 200. suppose that
38:30instead you divvy up the money so that k
38:32number of people each buy two on votes
38:35then you get square or spend two n
38:37dollars then you get k times square root
38:39of two n votes yeah and so it's
38:41increased by a factor of square root k
38:43yeah that's basically right so i mean
38:45there are two ways of okay so there's
38:46two different types of collusion imagine
38:48that one person is in favor of something
38:50and another person is against and they
38:52offset each other
38:53they could just make an agreement that
38:55neither of them will buy anything
38:57and then they save the money
38:59right
39:00so that's one way that you could collude
39:02but that's not going to impact
39:03efficiency right because that's just
39:05cancelling out two people would have
39:07canceled out anyways it's only affecting
39:09how much revenues are raised but what
39:10evan is suggesting is something that's
39:12more dangerous to efficiency and let me
39:14put it in a slightly different way than
39:15evan did imagine that we're both opposed
39:17to something we both wish the other
39:19person would buy more votes than they're
39:21buying
39:22so if we collude we'll both buy more
39:24votes in the direction that we both feel
39:27then we would otherwise
39:28you see what i mean
39:32um
39:33yeah
39:34one person would buy more and one person
39:36would buy less of the like total amount
39:39no that's not true because we both gain
39:42on the margin from the other person
39:44buying more votes
39:46right and once we take that into account
39:48we'll both buy more another way of
39:52stating that is what evan said which is
39:54that if you pull our utilities together
39:56now the cost of buying votes is
39:58effectively lower
40:00because we can spread it over the two
40:02people and therefore we only have to pay
40:05like one over m of the cost that we have
40:07to pay if we bought it completely
40:09separately yeah but then wouldn't you
40:11have like three writer problems if you
40:12had two people and they're both going to
40:14say favored one's voting a lot more than
40:15the other one they wouldn't want to like
40:17why would you want to increase their
40:18votes because one person would be like
40:20three already on the other person yeah
40:22so that's exactly right so under linear
40:25contributions to a public good we have
40:27the free writer problem but if you have
40:30quadratic payments for contributions to
40:32a public good there is no free writer
40:34problem it exactly offsets the free
40:36writer problem
40:37and so as a result of that if people
40:39then try to solve the free writer
40:41problem that actually hurts us so like
40:43before we had to like to get around the
40:46fact that like no under linear
40:47contributions we had a free writer
40:49problem we needed to get people to
40:50collude here now it's actually harmful
40:52that people are colluding because we've
40:53moved to a market system where we've
40:56offset fully the free rider problem
41:00so like
41:00here's another way of thinking about it
41:02if we have a system where you make
41:03linear contributions then um having like
41:08multiple one person broken up into
41:10multiple people is really bad because
41:12there's a free writer problem
41:14if contributions were
41:17like every person gets to make one
41:19dollar of contribution well then you'd
41:21want to be split up into as many people
41:23as you possibly can
41:24and quadratic is the point in between
41:26those two extremes where those two
41:28effects exactly cancel each other out
41:30like with the example you gave were you
41:31like two people they both up there
41:34yeah if they talk to each other they
41:36both decide like they both find out
41:38they're
41:38favoring the same thing wouldn't one guy
41:40say like
41:41well
41:42i mean that other guy's gonna look
41:43forward so like i don't have to vote as
41:45much like i'm less pivotal the other
41:47well so first of all
41:49they won't affect that much how much how
41:51pivotal they are but um
41:53but yeah they would have an incentive to
41:55defect from the collusive agreement just
41:57like every collusive agreement creates
41:59incentives to defect just like we
42:00studied
42:01yeah so
42:03yeah what about if uh
42:05someone if there's a
42:07if someone
42:08pays like a person who's relatively
42:10different
42:11say you know they don't really care so
42:13i'll pay you
42:14three dollars to uh to make a couple
42:16votes so you you like spread out your
42:18costing on all these people which will
42:20lower the total cost too you know if you
42:21bribe these people to make boats for you
42:23yeah so that those are people who don't
42:25care at all who are sort of weakly in
42:27this direction so it's a combination of
42:29the two effects right some of the
42:31benefit that you get from that is you
42:32get a cheaper way of getting the same
42:34number of votes but another incentive is
42:36because it's cheaper to buy votes you
42:37might buy more so both of those effects
42:39will come into play so would that be uh
42:42won't that be very bad for the system
42:44it would be uh yeah so that that's
42:46that's exactly the collusion problem we
42:48were talking about with evan yeah
42:50um
42:52okay so let me actually go through an
42:53example just like the one tanner said so
42:55imagine that romney wants to buy the
42:57presidency
42:59uh and he has a hundred thousand dollars
43:02to do do that like that's his wealth how
43:05many votes would he be able to buy on
43:06his own uh andrew
43:10ten thousand right
43:12now um
43:14note that that's not going to be do him
43:17all that much good probably doesn't even
43:18do him as much good as what he did
43:19through his advertising right because he
43:21only gets 10 000 votes and that's if
43:24everybody else spent on average one
43:25dollar that would be less than point one
43:27point zero one percent of the total vote
43:28in the u.s right now imagine he can get
43:31a hundred friends who otherwise wouldn't
43:33have spent anything to take each of his
43:35mill you know those million dollars
43:38uh they could each buy 1 000 votes and
43:41how many votes would that translate into
43:43in total jillian
43:44so that would be
43:46uh a hundred thousand votes yeah exactly
43:48but still that's only point one percent
43:50of the total vote and each one of those
43:52friends would have like a giant
43:54temptation not to spend those million
43:55dollars on that but instead to just
43:57pocket the money and say oh sorry you
43:59didn't win but you know
44:03you know
44:04uh
44:05it's also would be very easy to get
44:07caught because not only would those
44:09people have a temptation to run off with
44:10those million dollars but not only can
44:12they run off with it but they can also
44:13report it to the government the
44:14government would be like well if you
44:15were asked to be part of a collusive
44:16scheme report it to us and then we'll
44:18give you an extra million dollars as a
44:20reward right uh or mitt romney could
44:23pretend to be a hundred people right
44:26but uh obviously that would
44:29be a pretty dangerous thing for him to
44:30do yeah dave
44:32but i mean in this particular situation
44:36if you just issue like five dollars to
44:38every like hardcore republican voter
44:42i don't think the republican vote the
44:44typical republican voter they would want
44:46to vote for romney yeah but the thing is
44:48they would want to vote for romney the
44:50same amount that they wanted to vote for
44:51romney before they got those five
44:52dollars
44:55it just seems to me that like that that
44:57makes sense in the theoretical sense but
44:59practically speaking i feel like it
45:01would be i could easily imagine a
45:02scenario which they just gave out five
45:04dollars and at like the campaign like at
45:07the voting poll and then they just well
45:08i mean they could do that right now so
45:10like they could go around to everyone to
45:11get out the vote and they could just pay
45:13the money for no reason to say oh here's
45:15some money
45:17you know what i mean and there's still
45:18lots of people who don't vote
45:20i mean if they were doing it on a
45:22massive scale like that it would be at
45:24least as easy to catch as vote buying is
45:26right now
45:27right
45:28so
45:30uh yeah tanner what about if the voting
45:32was public because there's plenty of
45:33times like in the paper you brought up
45:35u.s congress if they did some like qbb
45:38for that yeah where it's easy to know if
45:40someone actually does
45:41yeah through when you bother about how
45:43they stop then it's definitely harder to
45:45stop collusion just as right now it's
45:46harder to stop like the bargaining in
45:48congress from corrupting things right uh
45:52you know you'd have to try to police
45:54that in other ways through norms that it
45:55was like really dirty or unethical to do
45:58stuff like that but
46:02um
46:02okay
46:04so
46:05um
46:07the other thing is that it's not just
46:09detection by authorities that can cause
46:11problems for this
46:13but if other people know that you're
46:15buying votes that actually creates
46:16incentives for them to offset what
46:18you're doing so then it can become
46:19self-defeating
46:22because like if they know that your side
46:23is likely to win now then they're gonna
46:25go against that
46:27okay so there's many other issues of
46:29robustness here yes hello
46:31but
46:32if you convince them that you've
46:34established an extremely strong position
46:36and they can't take it down on their own
46:38might they just give up because their
46:39density of pivotality falls to close to
46:42zero no so the opposite actually happens
46:44because all the other people that are on
46:46your side also have their density of
46:47pivotality that falls to zero
46:49and you have your density of pivotality
46:52falling to zero so you don't even want
46:53to buy that many
46:55and you see it starts to happen yeah so
46:57it's actually that's actually always
46:58against your interest you always want to
47:00convince people that they're likely to
47:02win
47:06um okay but let me breeze through a few
47:09different things so
47:10um
47:12uh
47:13there's a question of how many people do
47:14you need
47:15for things to actually be small and you
47:18can calculate this stuff and it's done
47:19in the paper i won't go through that
47:21what if people overestimate this should
47:23be p not g
47:24um
47:25like what if they think that they're
47:26more likely to be pivotal than they are
47:27like
47:28maybe that helps explain why people vote
47:30under our current system even though it
47:32takes some of their time this actually
47:34raises efficiency because it makes it
47:37more likely
47:39that um
47:41it makes it more okay so if you look at
47:44like what happens is like the number of
47:46people gets large the problem is there
47:47might be someone who's like really
47:49opposed to the thing who like buys out
47:51everyone else and because everybody else
47:53doesn't think a tie is very likely
47:54there's not enough of them to un
47:56overrule him but if they think the thai
47:58is very likely
47:59then that can't happen and so it
48:01actually makes the system more efficient
48:02yeah austin are
48:05papers have been there
48:06on trying to establish whether it is
48:07kind of overestimating the pivotality
48:09yes there's a huge literature on that
48:11there's also other reasons like people
48:13just want to express themselves through
48:15their vote they want to like say like
48:17i'm in favor of this person that also
48:18aids efficiency we went through like
48:20sort of almost all the models that like
48:22are typically used to explain
48:24this and and they all like actually make
48:26it work at least as well if not better
48:32um okay uh
48:36another possibility is that um rather
48:40than people differing in their
48:41preferences they might all have the same
48:43interest like we might all want being a
48:45you know have equal shares in the
48:46company and want the company to do well
48:48but different people might have
48:49different information
48:51and the nice thing about quadratic
48:53voting in that context is unlike
48:55standard voting where like all you can
48:57do is say yes no or abstain here you can
48:59say well i know a little bit in this
49:01direction but i don't want my vote to
49:02have too much weight i want to defer to
49:04other people right and so this lets you
49:06do that
49:09this
49:11does better in terms of incentives to
49:14acquire information as well so you won't
49:17necessarily acquire enough information
49:19for the same way as an intellectual
49:21property because if it benefits other
49:23people that information like if it
49:25doesn't affect only your payoff but it
49:27affects other people's payoffs you don't
49:29have enough incentive to acquire
49:31information but it does give you the
49:33right incentives to acquire information
49:35about your own preferences
49:39there's also the possibility that people
49:41don't know what p is because um there
49:44might be uncertainty about like overall
49:46how do people feel about this issue and
49:48this can lead to some inefficiency but
49:50it still almost always does better than
49:52democracy
49:53and polling and communication
49:55uh can help give people a sense of of
49:58what p is and and restore uh more
50:00complete efficiency
50:02okay
50:04so
50:05um
50:06there are alternative versions of this
50:08that you can do
50:10such as you don't need to use real money
50:12you can use
50:14fake money
50:16you can extend things beyond binary
50:18choices
50:19and you can help people figure out what
50:22p is
50:23and let me talk about some of those
50:25extensions so
50:26as i mentioned earlier if you want to
50:29decide between multiple alternatives the
50:30right way to do it is to have one
50:32default choice and then the other
50:35choices you can buy votes in favor of or
50:38against
50:39you can even allow people to nominate
50:41things and the way that they do that is
50:44they commit
50:45some of their money
50:47to buy votes and if you get enough total
50:49votes together then the issue gets put
50:51onto the ballot and then your money is
50:54committed to it once you've done that
50:55and that keeps people from as some
50:57people were mentioning putting up
50:58frivolous votes just to get
51:00redistribution back to them yeah julian
51:02doesn't
51:04undervalue the people who are
51:06trying to push the issues they have to
51:08spend
51:09time to get other people to like even
51:10learn about the issue and collect the
51:13money but but i mean it's also costly on
51:15other people to have to consider the
51:16issue and so that's what they're being
51:18forced to pay for basically
51:24so there are versions without actual
51:26cash because you can if there are
51:28multiple decisions
51:30or multiple choices within a decision
51:32then people can make trade-offs between
51:35those different things and so you can
51:36give people artificial currency that
51:38they can spread across those different
51:39decisions
51:40so that's one thing you guys might want
51:42to do if you're running into resistance
51:43to using actual money is if you have
51:45multiple decisions you can give people
51:47some tokens and then they can spend it
51:49on the different decisions
51:50or even if there's only one decision to
51:52be made if you have multiple options
51:54then you can give it to spend on the
51:56different options yeah when you take
51:58multiple decisions you're like
51:59there are multiple decisions across time
52:02right yeah everybody yeah exactly but
52:04even if you have like three options like
52:06you're gonna there's three different
52:07restaurants you're gonna go to you can
52:09give people currency and they can spread
52:10those across
52:12the two different alternatives to the
52:14status quo
52:16um
52:17okay
52:18you can also give guidance to voters on
52:20p so you could have everyone
52:21simultaneously report in their values
52:23and then you could have like a value of
52:25p that's being estimated by the computer
52:27and it could fluctuate around as people
52:28buy more or less votes as p rises people
52:30will buy more votes but then the chance
52:32that anyone's pivotal will go down and
52:34it will equilibrate at the right value
52:36of p
52:37um
52:38so it's sort of like a market right like
52:40if there's more demand the price goes up
52:41if there's less demand the price goes
52:43down
52:44uh yeah kristen what is this kind of
52:46guiding voters to the computer
52:48encouraged collusion up to the point of
52:50actually buying votes like under
52:52reporting
52:53well but the thing is it's just like an
52:54auction like people
52:56won't want to do that very much because
53:00they are worried that the auction might
53:01at any point end and then they're gonna
53:03get stuck looking like an idiot
53:05you see what i mean
53:07okay
53:08um so
53:10uh
53:11yeah
53:13like during the simulation they're not
53:14actually putting any money right so no
53:16they are that what they're at every
53:18point saying is like here's what i they
53:20say here's how much i care about the
53:23issue and then the computer will
53:24automatically given the value of p make
53:26you vote
53:28p times that
53:30you see what i mean
53:33okay
53:34so the easiest applications in the short
53:36term
53:37will be i think in the private sector so
53:40some examples of this there's
53:44there's a group of students
53:46led by a student who took this class
53:48last year jacob rabinowitz i don't know
53:50if anyone knows him
53:52and they're designing one that uses fake
53:55currency for the mobile app challenge do
53:57you guys know what the mobile app
53:58challenge is yeah so they're submitting
54:00an application to that
54:02that will be for committees using fake
54:04currency deciding on things like
54:06awarding honors to students hiring
54:08scheduling meetings etc
54:12other applications like this are book
54:14groups or clubs
54:18another
54:20application that we're exploring
54:22is
54:23startup companies like
54:25within the company deciding on amenities
54:28or investments that they're going to
54:29make corporate governance is another
54:32application so there's remember we
54:34talked about all these minority
54:35shareholder protections
54:36uh in one of the first classes um
54:39and
54:41those were like
54:43using very particular rules like if you
54:45get above 15 of shares then you need to
54:47like declare that and then other people
54:49can vote against you at a lower cost or
54:51whatever here you have a very simple
54:53system for down weighting large
54:54shareholders that can avoid them
54:57exploiting other people which is
54:58everyone just gets to vote the square
55:00root of the number of shares that they
55:01have so on the one hand you guys when
55:04you try to use this with your friends
55:05might run into objections that oh it's
55:08unfair that someone with more money
55:09should have more say
55:10but you get the opposite objection in
55:12corporate governance which is people say
55:14oh it's unfair that someone who's 20 of
55:16the shares shouldn't get 20 of the votes
55:18shouldn't they have say something
55:20exactly in proportion to how much money
55:22they have well no you know they should
55:24get the square root so in in both cases
55:27uh you know we get objections but coming
55:29from opposite directions but everyone's
55:31used to the conventional system and not
55:33used to
55:34this deviation from it
55:38okay so actually this is a big issue in
55:41korea because there are these families
55:44that control
55:45um these companies uh even though they
55:49don't have um that much of a like actual
55:52ownership stake they have a much larger
55:55voting stake and they do that by like
55:57having 51 percent of a company that has
55:5951 of a company that is 51 of a company
56:02that owns this you know the final
56:03company right
56:05um
56:06and uh they use that to like suck all
56:09the profits out of the company by
56:10forcing it to like uh
56:13buy very expensive services from a
56:15company that they own 100 of and as a
56:18result of that they want like some way
56:20to try to reduce the power of these
56:22large holders and what i proposed was uh
56:25using this quadratic voting uh system or
56:28square root voting uh as an alternative
56:31um and i actually presented in front of
56:33the national korean national assembly uh
56:36when i was there
56:38um but i think actually the most
56:40exciting applications are in the public
56:42sector
56:42so for example remember when we talked
56:44about eminent domain and complements
56:46assembly
56:47well a a
56:50natural
56:51system
56:52would be to have people
56:55buy
56:56votes on whether to accept an offer
56:58that's made to them by the government to
57:00buy out their land
57:02um and that is much more efficient and
57:04ensures that no one ever gets their land
57:06bought out for less than it's worth in
57:08total to the people who it's bought from
57:10international institutions right now are
57:13a total disaster i think as we've seen
57:15through like the syria events and so
57:17forth right um because there are all
57:20these tiny little countries that can
57:21paralyze the institution but on the
57:23other hand when there's an issue that's
57:25really relevant to one of those
57:26countries like israel or something like
57:28that then they can trample all over
57:30those countries sovereignty if con if
57:32countries could
57:34like by paying into the operations of
57:36the
57:37uh
57:38organization uh
57:40buy votes according to the square root
57:42this would be much more efficient than
57:44the way that it currently runs which is
57:45that the us goes around and offers like
57:48military aid to all the countries that
57:50vote with it
57:51in the u.n which is probably much less
57:53efficient than just funding the un's
57:55operations uh using the purchases of
57:58votes right
57:59um
58:00representative bodies could work this
58:01way too you know currently congress used
58:04to have all these systems of um
58:07you know pork barrel spending to buy off
58:11somebody else uh in order to get a bill
58:13passed and you know that was done away
58:15with by the bands on earmarks but i
58:18think a lot of people think that's made
58:19congress work a lot less efficiently
58:21and if you've seen the movie lincoln you
58:23know that like those buying the votes
58:25from different people is actually
58:28uh you know important to get legislation
58:30through
58:31and if people could actually just use
58:33money from their districts directly
58:36in you know paying out of that into some
58:39account that would be
58:42that would probably be more efficient
58:46eventually
58:48you could even use this for referenda
58:50and elections directly either with money
58:53or without money um
58:55and i know that a lot of people would
58:57object to you having like you know the
58:58rich have more sway in elections but i
59:01think that a lot of that comes out of
59:03mistaking linear vote buying for
59:05quadratic vote buying because as we saw
59:07with romney he could buy very few votes
59:09with all of his money
59:11once you have the quadratic rule
59:13and i think more broadly as we talked
59:15about when we were doing cost benefit
59:17analysis and so forth
59:19it's not clear why we should wall off
59:21public decisions from the influence of
59:23money that we have in private decisions
59:26that's not efficient because it
59:28basically forces poor people to have
59:30crappy schools bad health care
59:33but have equal say on whether abortion
59:35is legal or not
59:37uh it doesn't seem like that's in
59:39anybody's interest if you could make
59:41payments to people that would allow them
59:43to live better lives but have less
59:45influence say on social issues
59:47that would probably be uh you know
59:50better for everybody
59:51um
59:52and
59:55in fact i think money might well have
59:57less influence in some ways because
59:59right now you can linearly buy campaign
1:00:01ads that sway basically in different
1:00:04people whereas that wouldn't be as
1:00:05valuable under the system because if the
1:00:06people remain different they wouldn't be
1:00:08willing to put their money in and be
1:00:10swayed by those stupid ads right
1:00:13so as a result of this i hope that in
1:00:15the long term
1:00:16the this system could transform the way
1:00:20that a lot of different social
1:00:21organizations work but in order to do
1:00:23that we need to experiment a lot with it
1:00:26we need to figure out what you know how
1:00:28people relate to it what's the easiest
1:00:30way to get people to understand it uh
1:00:32yeah evan how exactly does this um work
1:00:34against advertisements so what if there
1:00:36is a particularly good advertisement and
1:00:39it sways 15 different people to go out
1:00:41and buy bugs well i think that the thing
1:00:44is that um
1:00:46if you get them to buy just a tiny
1:00:47amount
1:00:49right
1:00:50it won't have much of an effect so ads
1:00:53that are meant to appeal to sort of like
1:00:54ignorant and not like people who don't
1:00:57really care at all are not going to have
1:00:59much effect on the other end really good
1:01:01ads that generally provide really
1:01:02important information and really change
1:01:05seriously how much people care about
1:01:06something will have an effect but they
1:01:08should
1:01:09so that that's the point yeah austin
1:01:11what about like in variance of like how
1:01:13much people are going to pay like i know
1:01:14how we talked with survey mechanisms
1:01:16people always tend to go towards like 20
1:01:18likes for instance yeah
1:01:20uh wouldn't that tend to have an impact
1:01:22it wouldn't tend to suggest that maybe
1:01:23people wouldn't
1:01:24pick you know very very small numbers
1:01:27well i think that the
1:01:29the
1:01:32in surveys people usually aren't meant
1:01:33to put real money on the line and we do
1:01:36have a lot of evidence that when real
1:01:37money is on the line people are less
1:01:39subject to those types of effects so i
1:01:41think that's the problem with contingent
1:01:42valuation yeah question this might be
1:01:46could the quadratic buying be used in
1:01:49other applications like for example
1:01:50buying campaign ads i know that already
1:01:52yeah absolutely
1:01:54so here here's an alternative way to do
1:01:57that so
1:01:58imagine that um
1:02:00okay so right now like
1:02:02everyone thinks that the wealthy have
1:02:04too much influence on campaign ads that
1:02:06exist
1:02:07and that the poor have too little
1:02:09influence
1:02:10and sometimes people propose public
1:02:12funding of campaigns you know as a
1:02:14partial solution to that so here's a
1:02:16really simple way that gives voice to
1:02:18people over who gets to
1:02:21have what campaign ad but also is like
1:02:25um
1:02:26uh more egalitarian so imagine the
1:02:28government puts in a bunch of money and
1:02:30we have some
1:02:31multiplier where like if you pay
1:02:35x dollars
1:02:36x
1:02:37uh the square root of x times k
1:02:40dollars is donated to your political
1:02:42campaign so then the rich could
1:02:45put more in but it would be very very
1:02:47expensive for them to do it and the poor
1:02:50uh could put it in but it would be very
1:02:52cheap for them to do it because they
1:02:54would you know
1:02:56be spending a very small amount and
1:02:58would be multiplied by some big amount
1:02:59and to make the budget balance you would
1:03:01take whatever money comes out of the
1:03:02public treasury to subsidize the system
1:03:05and in fact that's a more general rule
1:03:07way of doing this so like if bill gates
1:03:09wanted to like contribute
1:03:11uh to charities but wanted to give you
1:03:13know harness the wisdom of crowds he
1:03:15could say here i'm going to give this
1:03:17money and i'm going to make up the
1:03:18difference between the square root times
1:03:20k and like the actual amount of money
1:03:22that people put in
1:03:24uh and that would be like an efficient
1:03:26way to figure out what the right
1:03:27charities are to give to
1:03:30um
1:03:31okay so we think that we need to start
1:03:33with the small applications learn from
1:03:36those and build out from there
1:03:38um and as a result eric posner and i
1:03:40have started a company that's trying to
1:03:42develop software to do this it's called
1:03:44collective decision engines
1:03:46and some undergrads as i mentioned have
1:03:48been very involved in the development of
1:03:50this
1:03:51the basic ideas behind it are
1:03:53public but the
1:03:55implementation will be proprietary and
1:03:57the saw the problem set has you sort of
1:03:59play with
1:04:00uh working on this uh to try to help us
1:04:03out a little bit
1:04:04uh we plan to use this to you know
1:04:07learn and improve so please give us you
1:04:10know feedback and i'm looking forward to
1:04:11seeing your solutions on the problem set
1:04:13um
1:04:14and this will help us tailor
1:04:16um
1:04:17uh things to application sorry if we
1:04:20succeed we're going to try to tailor the
1:04:22system to particular applications
1:04:25that will allow us to bring in some
1:04:26revenue
1:04:28and
1:04:29thereby continue to improve the system
1:04:32market it uh and increase the level of
1:04:35ambition that we um that we go for okay
1:04:38so i think that this is one example
1:04:41of how economics can change your
1:04:44thinking
1:04:45about uh issues the course tries to be
1:04:49sort of a back and forth between
1:04:50economic paradigms and real world
1:04:52applications of them and let me try to
1:04:54remind you of some of the breadth of
1:04:56things that we covered we talked about
1:04:58some of the surprising dynamics of drug
1:05:00markets we talked about incentive
1:05:02schemes in managing organizations about
1:05:04optimal carbon taxation the regulation
1:05:07of the insurance industry the design of
1:05:09auctions and criminal justice solutions
1:05:12to complementary goods assembly and
1:05:15holdout problems and eminent domain we
1:05:17talked about innovation policy merger
1:05:19control
1:05:20income taxation new ways of collective
1:05:22decision making and in all of these
1:05:24areas i hope that you guys now have
1:05:26something interesting and different to
1:05:29say from an economic perspective that
1:05:31you wouldn't have thought of otherwise
1:05:32about what uh optimal policy should be
1:05:35on all these types of questions
1:05:37we also tried to explore some
1:05:39fundamental trade-offs
1:05:41about which i hope you now have more of
1:05:43a nuanced and less ideological
1:05:45understanding we tried to think about
1:05:48you know disaggregating some of the
1:05:49differences between quote capitalism and
1:05:51quote socialism
1:05:53such as the trade-off between
1:05:55internalizing externalities
1:05:57and providing public goods that on the
1:05:59one hand there are distortions from
1:06:01ignoring those externalities but
1:06:04standard political systems are very
1:06:06flawed ways of making decisions about
1:06:08those and so that creates a really big
1:06:10trade-off
1:06:12redistributing income
1:06:14is beneficial because it provides social
1:06:16insurance but it can reduce incentives
1:06:19of people to work
1:06:23instituting regulations that eliminate
1:06:25the distortions of market power
1:06:28or providing prizes in lieu of patents
1:06:30can be beneficial but it also requires
1:06:32the government to have a lot of
1:06:33information that might not be available
1:06:36competition policy can
1:06:39reduce market powers of cartels
1:06:42but it can also eliminate economies of
1:06:44scale
1:06:45and perhaps get in the way of
1:06:48innovation and creative destruction
1:06:51so not all of these issues are the same
1:06:53and they depend on different parameters
1:06:54in different settings that you know are
1:06:56adapted to different circumstances and
1:06:58so i hope rather than just having an
1:07:00ideology in one direction or the other
1:07:02you guys will come to have had a more
1:07:04nuanced sense
1:07:06of
1:07:07each of these issues and that this will
1:07:10allow you to combine in your
1:07:12person both the character of the expert
1:07:15that we talked about and of the voter
1:07:17and thereby
1:07:19help make you more informed participants
1:07:22um in
1:07:24many ways in a wide variety of social
1:07:26issues and i think this brings us sort
1:07:29of to the end of the course and what
1:07:30this all means to you
1:07:32and let me just tell you a little bit
1:07:34about my story and how i got interested
1:07:36in economics because maybe it'll mean
1:07:38something uh
1:07:39in this context so i worked at a hedge
1:07:42fund during the summer of 2005 which was
1:07:44sort of at the height of the uh boom in
1:07:47the financial industry and we developed
1:07:50a trading strategy that made a lot of
1:07:51money but seemed for reasons that you
1:07:53guys sort of explored during the class
1:07:55uh actually socially destructive to me
1:07:58and i asked my boss you know what was
1:08:00the value for which we had been rewarded
1:08:02with whatever 200 million dollars and he
1:08:04said ours is not to question why ours is
1:08:07just to do and die
1:08:09and so that
1:08:11day
1:08:12i
1:08:13had dinner with the person who became my
1:08:15advisor who was my teacher uh in my one
1:08:20of my economics courses and i told him
1:08:22the story and he said look if you become
1:08:24an economist your job will be to
1:08:25question why
1:08:27and that's why i decided to be economist
1:08:29by becoming an economist
1:08:31and you know the way i think about it is
1:08:33that the you know society is like a
1:08:35giant machine
1:08:36and there's lots of people who have to
1:08:38work very hard just to you know keep one
1:08:40of the parts of the machine turning but
1:08:42we need
1:08:44uh and because we're such a wealthy
1:08:46society now we can now afford to have
1:08:48somebody who has you know some
1:08:50small class of people
1:08:52who ask questions about whether the
1:08:54machine is working well and whether
1:08:56things should be moved around to make it
1:08:58work better
1:09:00and to me it's an incredible honor to be
1:09:03part of that small class of people who
1:09:05gets to ask those questions about how
1:09:07changing social arrangements
1:09:09might
1:09:10make society
1:09:12work better
1:09:14and
1:09:14from my perspective those types of
1:09:16questions are really writ large across
1:09:18the face of history they're the
1:09:20questions that people have been asking
1:09:22for thousands of years and that people
1:09:24will go on asking as long as mankind
1:09:27doesn't manage to wipe itself off the
1:09:29face of the earth
1:09:31and
1:09:32you know you might think that economic
1:09:35ideas are just abstract ideas that never
1:09:37change policy
1:09:38uh and to some extent maybe that's true
1:09:41uh but to me there are so many
1:09:43politicians and so many activists who
1:09:45believe they know to make the world
1:09:46better but who've really never taken the
1:09:48time to reflect on the contradictions in
1:09:50their own views
1:09:52and as an economist just the joy of
1:09:54seeing a logically consistent way that
1:09:56you could actually make the world better
1:09:58is quite beautiful in and of itself
1:10:01and in the longer term i'm not sure how
1:10:04useless those ideas are if you think of
1:10:06john maynard keynes if he had gone and
1:10:08spent all of his time trying to persuade
1:10:10roosevelt to deficit spend
1:10:13maybe he would have accomplished a
1:10:14little bit but probably not very much
1:10:16and world war ii came along anyways and
1:10:18in the long term he changed how all
1:10:20governments in the world work and now
1:10:23things that you just take for granted
1:10:24that you think are so practical like of
1:10:26course the government should spend
1:10:28during a recession
1:10:29were totally crazy at the time that he
1:10:32was proposing them so um
1:10:35keynes famously said that you know
1:10:37practical men uh who think that they're
1:10:39just going on what common sense says
1:10:43are usually the slave of some economist
1:10:45who died a hundred years ago
1:10:48and on the other hand the radical
1:10:50ravelrouser uh who you know hears voices
1:10:54in the air
1:10:56you know to lead to a revolution is
1:10:58probably also listening to an economist
1:11:00who had a debate with that other
1:11:01economist a hundred years ago
1:11:03um
1:11:04you know if you think of
1:11:06uh athens and you went to someone in
1:11:08athens they would have said you know
1:11:09what are the most important you ask them
1:11:11what are the most important things going
1:11:12on and they're like well pericles just
1:11:14handed over the general ship to this
1:11:16other person whose name we don't even
1:11:18know anymore
1:11:19and you know that was a really big coup
1:11:21and you would have said well what about
1:11:22this guy who's walking around all the
1:11:23markets asking people questions
1:11:26about you know morality and life and
1:11:29education
1:11:31and they would have said well
1:11:32everybody's got their entertainers and
1:11:34crazy you know
1:11:36academics but those people really don't
1:11:38have much say on anything and 2 000
1:11:41years later socrates is the foundation
1:11:44of the civilization we all live in and
1:11:46uh you only learn about pericles once
1:11:48you come and take an ancient history
1:11:49course at the university of chicago
1:11:52so um ideas have a long gestation period
1:11:56but in the end uh i think in the long
1:11:58term uh very little matters and i think
1:12:01democracy is a perfect example of that
1:12:03something that seemed like a completely
1:12:04crazy form of government 400 years ago
1:12:07is now completely axiomatic that of
1:12:10course that's the only way we can run
1:12:11anything and anything else that you
1:12:13suggest is completely crazy and
1:12:15subversive so uh i hope that you guys
1:12:18will consider engaging serious with the
1:12:20life of the mind seriously with the life
1:12:22of mind even if you don't
1:12:23end up
1:12:25becoming
1:12:26economists or anything like that so
1:12:28thank you

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