(Quadratic) Vote Selling

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Dale Sheldon-Hess

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Jun 5, 2013, 6:57:15 PM6/5/13
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Just saw this, thought folks might have opinions:

http://www.slate.com/articles/news_and_politics/view_from_chicago/2013/06/new_york_s_bike_share_try_quadratic_vote_buying_to_figure_out_if_people.html

"Under QVB, each person has the right to buy as many votes as he wants
at a price equal to the square of the number of votes that he buys:

"The outcome is determined by majority rule, based on this method of
vote calculation. If Anne buys eight votes in favor of the program,
Bruce buys four votes against, and Carla buys two votes against, then
the program is approved by a vote of eight to six. By contrast, with
ordinary voting the project would be rejected two to one. Voters vote
and pay through a mobile app or website.

And then their payments are distributed—to each other, in equal
shares. Anne paid $64, Bruce paid $16, and Carla paid $4, for a total
of $84, and now each person receives a third of that total, $28."

--
Dale

Warren D Smith

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Jun 5, 2013, 8:09:24 PM6/5/13
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One obvious problem is buying votes thru proxies. If Donald Trump
wants to buy 1000
votes, he could pay $1000000. Or, he could pay 1000 proxies $50, asking each
to buy 5 votes for $25 and keep the other $25. That way he gets 50,000 votes
(50X as many) but pays 50,000 (20X less money).

The incentives to do this, are thus enormous.

In theory maybe prosecutions and/or secret ballot could stop that.

I'm not actually seeing an argument for why "quadratic" is optimal. I
presume there is supposed to be one?

--
Warren D. Smith
http://RangeVoting.org <-- add your endorsement (by clicking
"endorse" as 1st step)

Warren D Smith

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Jun 5, 2013, 8:12:25 PM6/5/13
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I see now that there is a paper here:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2003531
and there indeed is a sense in which quadratic is optimal.
(This scheme is unconstitutional, that's another issue.)

Warren D. Smith (CRV cofounder, http://RangeVoting.org)

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Jun 6, 2013, 12:45:05 AM6/6/13
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OK, attempting to read+review paper:
E.Glenn Weyl: Quadratic Vote Buying
   http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2003531

It begins by warning "many of the results are conjectural" and 
hopefully proofs will be added later.  (Strange.)
The paper is poorly written (e.g. 
theorems involving undefined terms), intricate with
a lot of buzzwords, journalese, and random-looking math, and very long (57 pages)
making it hard to provide any rapid verdict. And I guess if and when he does add the 
missing proofs it'd then be 100 pages long?
  
(Nevertheless I will find a flaw that invalidates
his entire paper as currently written.  But I do not pretend to have completely 
digested the paper.)

Weyl's method is only intended for "binary" decisions, not 3-or-more choice elections.
That's a major handicap.

Weyl's method:
Each voter pays N^2 dollars for N votes.  (N varies with the voter.)
Side with most votes wins.  After election over, all monies
are divided evenly among all voters so in net none is lost, although there is redistribution.
The number N of votes can be any real>=0, it does not need to be an integer.

Weyl near start says he does not intend to convince us his method is "optimal" but rather
robust and simple and practical. 

The notion of optimality hinted in the abstract is this.  If you have bought N votes,
but want to buy N+1 instead, you need to pay 2*N+1 extra dollars.
You will consider this worth it if this 2*N+1 cost is less than the money benefit for you if
your side wins election.   In which case you do it.   Hence eventually we reach an "equilibrium" state 
where everybody has paid nearly that much, and say it then is nearly balanced election --
then you ask "what if I just bought 1 more vote and that tipped it?"
And you do so if 2*N+1<benefit, and hence this final move involves each voter putting
in a number of dollars proportional to her benefit (given that we ignore 
the "+1" as comparatively tiny), and hence the most-benefitted side 
wins, which is optimal outcome, QED.

Well, that reasoning seems a crock... but a funny thing happened when I wrote down 
the explanation of why it was a crock:
 1.  I've paid $1000000 to buy 1000 votes and am willing to now pay an extra $2001 to
buy 1 extra vote because the election win is worth $2003 to me.
     Bullshit.  In reality, I'd never pay the $1000000 in the first place.
  2. Linear, not quadratic, vote buying under his normal vote-total assumption
means my chance of altering election is proportional to my #votes is proportional to my $ spent.
That not quadratic seems to cause "optimality"... except say my chance of altering
election is c*N if I spend N dollars, where c=0.00000001.   Under those circumstances, is
it worth me spending ANY amount of dollars?  If I spend X dollars and
the election is worth $1 to me (if win) then I get  c*X expected benefit at cost X,
so no, spending anything at all was not worth it.
  3. Aha, but now we see Weyl's point!!  Say my chance of altering election with
his quadratic system is c*squareroot(N) if I spend N dollars.  This IS worth me
spending money on, because of the vertical asymptote of the squareroot function at zero.
My expected benefit (if an election-win is worth $U to me) is 
U*c*sqrt(N) versus cost=N, and the former is larger if N is small enough
(for any c>0 no matter how tiny).    Solving c*U*sqrt(N)=N for the point where cost=benefit
we find that  N=(c*U)^2  is the max amount of money I should spend voting.

It sure would be nice if money were real numbers, not discrete, because in reality it is discrete
(1 cent is minimum spendable amount) and that in view of the tinyness of c and the fact U
for many people is small, probably invalidates the whole idea right there since most people
are being asked to spend, say 0.00123 cents.  (I did not notice Weyl mentioning this
whole discreteness issue.)  But hey, let's improve the world to allow
continuum money to solve that, and continue on under that assumption.  [Or solve this
by demanding K*N^2 dollars for N votes, where K is some LARGE preselected constant...
except then you may run into other problem almost  nobody wants to vote.]

If everybody does that, then the number of votes on each side will be proportional
to the sum of the U-values on that side (i.e. utility sum) and hello -- optimality: the
max utility side wins the election.

[Course, there also is some redistribution of money, but it tends to be from richer to poorer
which is utilty-sum-increasing if utility is a concave-down increasing function of money.]

So that is the deeper explanation of why Weyl's system is "optimal" in a balanced
election situation with a normality-assumption.

Now what if we had an UNbalanced election where it was clear which side was going to win. 
The probability of an unexpected election result is exponentially tiny like 10^(-100).
In that case neither side finds it "worth it" to vote more than an exponentially tiny amount of dollars.
So I guess in that case, Weyl would say (or hope) the 
result was inevitable, it happens, and hardly any money was lost, so that's "optimal" too.

By the way, note what I just said was one hell of a lot shorter than 57 pages.  
So why the 57 pages?
Apparently because Weyl has an overpowering desire to suck up to 
everybody in every economics department in the world,
in vast preference to being simple and clear. 

In sec 4.4 Weyl discusses the "de-merger" problem where it is far more cost effective under
his system to buy votes thru lots of proxies.  There is a huge incentive to do that, which
might undermine whatever claims his system supposedly has going for it.
I had anticipated he was going to say "secret ballot" 
here but he does not.  I also thought he would argue the more people you use, the bigger 
your risk of being  caught, and some kind of prosecution risk would worry you.  
But he does not say that either.
He says "de-merger into two individuals... is probably all that is feasible in most cases"
for some unknown reason.  I can tell you that the Kansas City machine that elected Harry Truman
maintained registration lists of huge numbers of fake voters, comparable to or
outnumbering the real voters in the city.  And they controlled the judges (Truman was one)
hence not worried much re prosecution.

Weyl never mentions the 24th amendment, which is what 
says his scheme is unconstitutional in USA.
(It would appear that minor little things like US history and US constitution are of no 
importance to Weyl.)

Near the bottom of p.7 Weyl makes a flat out false statement about central limit theorem.  Since
his entire paper rests on this false statement that is not good.

The false statement is:
"the sum of values of all but one individual converges [to a normally distributed random variable] by the central limit theorem...when the number of individuals, and hence the variance... grows large."

This is false. False. False. Period. Full stop.  Complete and utter garbage.  It invalidates
Weyl's entire paper right there.

It is NOT the case, that a sum of random variables converges to a normally distributed random variable
(after rescaling).
Period.

But it would be true if, say, the summands all were identically independently distributed random variables
each with identical bounded variance and mean=0.   But Weyl explicitly assumes that his 
values are NOT identically distributed.  And they sure seem unlikely to be independent either.

In particular, suppose person number M (M=1,2,3,...) has value +-1/M with the +- sign
got by a random coin flip. This way we get total independence because I am extremely 
generously handing that to Weyl for free out of the kindness of my heart.

Now I will further, also extremely generously, let M--> infinity (infinite population) 
going right to the limit immediately.

Then: Is it the case that  SUM(for M=1,2,3...)OF  (+-1)/M
is (after some rescaling) a normally distributed random variable?  NO.  Is it the case
that its variance goes to infinity?  NO. 

And might a power-law distributed society like that be a reasonable model of a society?
Quite possibly.  It is observed that many ecosystems involve such power law distributions.
It also is observed that, e.g. "80% of the wealth is owned by 20% of the people" 
and empirical economic laws of that nature, which note ARE power law distributions.

Sorry Weyl.

Is this flaw fatal?  Not necessarily. I do not think Weyl actually ever really
needed normality.  All he needs is there be SOME limit distribution 
which in an unbiased election situation
looks uniform near the balance point.   The uniformity would be generic behavior for any 
probability density with a smooth CDF.  The existence of a limit distribution is not
obvious.

Still, it is not a promising start to have him shoveling hafalutin and false baloney at you,
when actually all he needed was to talk about generic behavior... if he can get existence
(which I'm not sure he can).

Now above, I spoke of two cases "balanced" and  "very unbalanced" elections.
But what is probably most interesting is a third intermediate case  where say
the 2nd option is probably going to win, say with estimated chance 70%, but not
enormously near 100%.   Then what?  In that case, your chance of altering election
might behave noticeably nonlinearly as a function of your number of votes.
In that case the argument quadratic ==> optimality is not exactly true anymore.

But the whole quadratic voting system should not behave too badly.

Other incidental notes: Clarke-Tideman-Tullock voting is discussed here including some ideas Weyl did not
mention:

A quadratic-voting idea for forcing honest utility-revelation was invented and explained here by me
sometime before 2009 but for that purpose seems supplanted by this:

So in conclusion, while I've been kind of nasty in this review, I think Weyl is correct 
that his proposed system is fairly simple, and would look fairly reasonable and practical
at least if we had continuum money, no US constitution, and if "paying for votes"
and "reliable uncorrupted secret ballots" were compatible notions.   And I also think his optimality
argument at its core after you strip  the bullshit away, contains a goodly amount of 
approximate truth.





Warren D. Smith (CRV cofounder, http://RangeVoting.org)

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Jun 6, 2013, 8:01:26 AM6/6/13
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Another issue with quadratic vote buying is this.

Suppose the "bInary decision" is "should we kill everybody who goes bankrupt, and abolish, e.g. food stamps?"
The people most affected by (i.e with the most utility at stake in) this election... do not get to vote!

The underlying problem there is the assumption (which a lot of economists take for granted) that utility=money.
It doesn't.

So anyhow, this example illustrates in stark terms the fact that quadratic vote buying it not necessarily
always going to work pretty well.   In http://rangevoting.org/CTT.html
I had argued that stockholder corporate votes might be a better use of Clarke-Tideman-Tullock voting,
than "real" votes.   Perhaps there is some friendlier setting for quadratic vote buying somewhere too.



Warren D. Smith (CRV cofounder, http://RangeVoting.org)

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Jun 6, 2013, 9:32:52 AM6/6/13
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The handicap of quadratic vote buying that it only works for "binary"
decsions, can largely be overcome. Here is one way.

Have voters vote on all (C-1)*C/2 candidate pairs (for C candidates for election).

Now recall in the model, that the vote difference is proportional to summed-utility
difference (approximating money=utility).
Hence, to the extent model is valid, then no preference cycle will be possible:

Hence there will be a unique "Condorcet winner" W, and then we
extract all the monies from the "W versus X" pairwise races like usual.

But since the model is not really 100% valid, cycles could exist.
That would be interesting as a revelation of its non-validity.
But anyhow, we then choose the winner W, such that 

    sum(over W's rivals X)OF   votecount(W)-votecount(X)

is maximal.  This chooses the max-utility winner (to the extent model is valid).
We then collect monies as usual for W-versus-X pairwise races.

Warren D. Smith (CRV cofounder, http://RangeVoting.org)

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Jun 6, 2013, 9:34:58 AM6/6/13
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Warren D Smith

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Jun 6, 2013, 10:23:49 AM6/6/13
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Actually, my all-pairs suggestion for generalizing quadratic vote
buying (QVB) to C-candidate elections, C>2, now seems busted or in big
trouble.

The problem is that in close pairwise elections there will be a lot
more voting/buying than in "easy call" elections. So my maximizing
proposal might favor a candidate who slightly wins a lot of close
elections, over one who wins a lot of pairs by huge margins. Oops.

The problem was the vote-difference=utility-difference model works well in
close but not in landslide elections.

---------

OK, another approach might take some elements from
http://RangeVoting.org/PuzzRevealU2.html
... e.g. you could do something like, run both QVB and a conventional
voting system, and QVB binary-chooses the winner from the top 2
finishers in the conventional system.
To the extent QVB is an "optimal" system this should be an improvement
versus the conventional voting system. On the other hand to the
extent QVB has serious
flaws versus some more conventional voting method (like the "kill the
people who have no money" vote), this should protect us from the QVB
monster. So this kind of hybrid system might (a) overcome the binary
limitation of QVB, while (b) potentially being actually better than
either conventional voting or QVB alone.

Or at least you could try to hope for that utopia.

Warren D Smith

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Jun 6, 2013, 11:21:48 AM6/6/13
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Actually, it strikes me that USA elections right now already
bear a great resemblance to Quadratic Vote Buying (QVB).
I'm serious about that although this will be pretty
amusing (at least if you have my sick sense of humor).

First QVB is for binary choices -- USA elections right now involve no
third choices... check.

People right now attempt to "buy" votes using political $ contributions.
If you donate N dollars, that effectively buys some function f(N)
votes, and the plot
of f(N) looks remarkably similar to the plot of squareroot(N).

I mean, if I hear 10 times more crappy political ads, I don't think that
gives you 10 times more chance I'll vote for you. I think it gives you less.
So the plot has a concave-down character just like squareroot. And just hearing
one initial ad can have a lot of effect, especially if it has
something new, i.e.
the initial money really has a larger, even huge, effect, just like
the squareroot function
has a vertical asymptote at 0.

Now in QVB they can try to cheat by voting through paid proxies. Similarly
in USA today, the Koch brothers etc continually try to hide
their monetary donations through a multiplicity of front groups
with disguised sources, and money-laundering groups like crossroads GPS.

So the two systems actually are very similar. (Enjoy optimality, folks.)

And there may be some lessons Weyl can draw from that...

Abd ul-Rahman Lomax

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Jun 6, 2013, 1:43:35 PM6/6/13
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One problem is that transfers are assumed to be
cost-free. In reality, there are two major hidden expenses:

1. The time that voters spend in the process.
2. The cost of funds transfer.

I haven't followed the argument as to why this is superior to straight bidding.

The method appears to provide an advantage to
collusion, since two voters can double their bid
for double the cost, instead of quadruple; it's
waved away, and perhaps that explanation is cogent, but it wasn't obvious.

Okay, net cost to Anne of $36 from example; so,
instead, Anne and Dummy buy eight votes, four
each, for a total cost of $32. They get the same
result as to the outcome. Total paid in: $52.
Refund, $13. Net cost to (Anne, Dummy), $6.

That is a very large incentive to create socks or
to buy votes. If Dummy is a real person, Anne
could pay Dummy $15 and be way ahead.

Perhaps I don't get it.

By the way, Warren has said that this proposal is
unconstitutional, based on the U.S. federal
constitutional prohibition of poll taxes. First
of all, this is not a poll tax, per se, so that
may not apply. Citizens would have the right to
*bid* (and a minimum bid could be free to
citizens. One cent? The state already pays
substantially more than that in election costs.)
Perhaps more importantly, the constitutinoal
prohibition only applies to certain elections,
specifically, various
Presidential/Vice-Presidential elections, and
Senateorial and Congressional elections.

Warren D Smith

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Jun 6, 2013, 12:50:50 PM6/6/13
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>By the way, Warren has said that this proposal is unconstitutional, based on the U.S. federal constitutional prohibition of poll taxes. First of all, this is not a poll tax, per se, so that may not apply. Citizens would have the right to *bid* (and a minimum bid could be free to citizens. One cent? The state already pays substantially more than that in election costs.)

--voting at all always costs money with QVB hence unconstitutional.

I am not necessarily opposed to vote-with-money schemes, although I
daresay I'd be opposed to at least some -- but anyway they are
unconstitutional, of that I have no doubt.

Warren D Smith

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Jun 6, 2013, 1:12:40 PM6/6/13
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An extension of Weyl's QVB idea is this.

Suppose that a voter has wealth W. The voter now spends some
amount A of her wealth on vote-buying.
Under the naive approximation that utility=money combined
with certain modeling assumptions, QVB yields a utility-optimal election
result.

However, we can use a less-naive approximation that the
voter's utility loss from spending money A is a function of BOTH A and W.

This leads to a more-general kind of quadratic vote buying which is:
the cost A for a voter with wealth W to buy N votes (0<=A<=W), is
A=f(A,W)*N^2
where f(A,W) is some appropriate function. This implicitly determines
the cost A.

To keep the revised plan simple: basically it costs less to buy votes
if you are poor,
but aside from that it still is quadratic vote buying.

The point is, that this way we can still get utility-optimal election
results under
Weyl-like modeling assumptions, but under a much better approximation
than utility=money.

Of course now voters could fake their wealth W, which would be yet
another kind of election fraud option.

Abd ul-Rahman Lomax

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Jun 6, 2013, 2:14:49 PM6/6/13
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At 11:50 AM 6/6/2013, Warren D Smith wrote:
> >By the way, Warren has said that this proposal is
> unconstitutional, based on the U.S. federal constitutional
> prohibition of poll taxes. First of all, this is not a poll tax,
> per se, so that may not apply. Citizens would have the right to
> *bid* (and a minimum bid could be free to citizens. One cent? The
> state already pays substantially more than that in election costs.)
>
>--voting at all always costs money with QVB hence unconstitutional.
>
>I am not necessarily opposed to vote-with-money schemes, although I
>daresay I'd be opposed to at least some -- but anyway they are
>unconstitutional, of that I have no doubt.

1. Yes, for federal elections, unless a feature were added. As I
didn't need to say, there are lots of elections that are not federal elections.
2. QVB is designed for yes/no decisions, which never occur in federal
elections anyway. (But, of course, an approval election is a series
of yes/no questions.)
3. I mentioned that, easily, the right to vote could be guaranteed.
The minimum bid could be paid for by the state or organization. I
mentioned one cent. Notice that the voter can choose which side to
vote on, and receives the payment regardless. So right to vote, here,
could be, easily, a right to receive a payment the same as all other
voters. Indeed, it could be more than a cent that is provided. Notice
that the voter is already investing more than a cent in labor to
vote, that's one of the unvalued costs here. (Desperately poor people
won't work for fifteen minutes for a penny, not in the U.S., anyway.)
4. I'm not approving of the system; reducing utilities to cash values
is highly questionable in many cases. I *do* recognize that is is a
measure of utility, simply not the only one and not necessarily
commensurable with other measures.

Executive summary:

1. I'm right.
2. You are wrong.
3. We have no doubt, on that we agree.

And now for something completely different....

(Seriously, I have not said that the proposal would actually be
constitutional, just that the issues aren't quite as simple as
Warren's comment might have made them seem.)

Warren D Smith

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Jun 6, 2013, 6:26:41 PM6/6/13
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One interesting limit of E.Glenn Weyl's system is a country in which 1
rich guy owns everything and everybody else owns nothing. His voting
system would in this limit
be a "dictatorship" since only one person could cast a nonzero vote.

The problem here again is the fact that utility does not equal money.
The modification of Weyl's system I sketched where utility can be an
arbitrary function of wealth need not necessarily have a problem even
in such limits (actually it probably
would have a problem, but for nonmathematical reasons :).

Warren D. Smith (CRV cofounder, http://RangeVoting.org)

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Jun 6, 2013, 6:50:44 PM6/6/13
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E.Glenn Weyl emailed me and seemed irate re my critiques, though
after a while I may be getting through to him, I don't know.

Anyhow, I suggested Weyl join CES & recruit others.  He said
he was in the process of forming his own science-based voting 
reform organization (or more than one!) instead.
He did not say what it/they would do, etc etc, but I presume his quadratic vote
buying will play a big part in it(?).  Maybe he will tell us.  I have no idea
whether these organizational moves by Weyl are a good or bad thing.

Weyl also remarked re voting reform organizations like the CES:
"My view is that they had no plausible practical suggestions.  I believe QVB is such."
which seemed to me rather radical.  My personal view is QVB may be good, but it'll
take a lot more to convince me or most anybody of that, several years
more research at a minimum, and his paper was not ready for prime time
and popular publicity. Plus it's dead meat for USA use due to 24th 
amendment, best prospects would be some other country I guess.  (China?)

Later Weyl elaborated that stuff like score voting  "are moderately plausible but I do not think they generally outperform simple voting and they are less familiar and more complicated. I do not claim that it would generally do worse; I just think that its benefits are not large or robust enough to overcome natural public resistance to the unusual."

Anyhow, Weyl like many voting beginners think they know more than they do (the problem is 
everybody thinks voting is simple and their intuition is obvious, but actually, non-inituitive things
are all over voting, I've never seen or heard of anybody whose intuitions re voting were always correct,
including me).  In the preceding paragraph he is working from intuition in the total absence of data
(which in fact seems to contradict him) but that's only one example.


Warren D. Smith (CRV cofounder, http://RangeVoting.org)

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Jun 7, 2013, 2:23:48 PM6/7/13
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Another extreme limit case of the QVB system with bad behavior is this vote:

"Should we elect Adolf Hitler dictator?"
Hitler organizes, say,  P/10 people (P=population) to each 
vote for him using  W*10/P votes each,
where W is "all the money in the country."  Then as dictator he would 
have no problem paying for it.

In another development -- I had thought based on the Posner Slate piece that started this 
QUOTE
recently, however, an economist at the University of Chicago named Glen Weyl has 
developed an ingenious new mechanism that is simpler and more robust, and could 
help a city decide whether to introduce bike sharing. He calls it Quadratic Vote Buying...
END QUOTE
that Weyl was the inventor of QVB.  However, this shorter paper:

Jacob K. Goeree and Jingjing Zhang:
Electoral Design, one man, one bid,

which Slate had not mentioned, but which Weyl (mis)cites,  introduces the same idea and presents
the same sort of optimality theorem, and also does some experiments with real voters.
(I suspect, however, that their "real" voters did not include, e.g, a single homeless person.)
They do not cite or mention Weyl.  So probably (?) it is they who were the real inventors.

The good news is, the Goeree paper contains two theorems.  The bad news is, 
each theorem uses undefined terms, I have a counterexample to theorem 1, 
and I have found at  least two reasons the proof of theorem 2 is wrong.

Details:

Proposition 1. For any symmetric value distribution, the fraction of the total surplus 

realized by majority voting falls from 1 when the size of the electorate is one to

...

which is less than 1 (for non-degenerate distributions) by Jensen’s inequality. The total 

surplus loss Wvoting-Woptimal diverges in the limit.

Problems:
What is "symmetric"? What is "value distribution"?  What is "total surplus"?
What is "Woptimal"? What is "
non-degenerate"?   

They never define any of these.   There is a reason theorems only shoudl contain defined words
and explicitly stated assumptions.  What if I produce a counterexample to theorem? Will they then say
"wasn't really a counterexample since (moving definitions and unstated assumptions)"?
This is not science.  Science is falsifiable.

But anyhow, one counterexample to theorem 1 is:
  N voters. Throw N dice and flip 1 coin (all i.i.d. fair).
If coin=heads, every voter has value in {1,2,3,4,5,6} where Mth
voter's value arises from dice M.    (+ values mean pro vote.)
If coin=tails, every voter has value in {-1,-2,...,-6} similarly.
This is a symmetric nondegenerate value distribution.
In the limit, the majority vote will 100% of time have zero regret 
(vote outcome favored by all always) and
hence the "less than 1" conclusion of theorem is false.
QED.

Next, we move on to their only other

Proposition 2. The bidding mechanism is budget balanced and individually rational. For large

which is independent of voter i’s own bid. For large

electorates, truthful bidding constitutes a Bayes-Nash equilibrium and

   limit (n to infinity)of   Wbidding//Woptimal = 1
Furthermore, voters of (almost) all types are better off under bidding compared to voting.


Problems:

what are "individually rational," "Bayes-Nash equilibrium," and "almost"
and "types"?  Again these are not defined in the paper.
But this proposition actually has a proof provided, unlike propo 1.
Whoopee.  But the proof is bogus:

QUOTE FROM PROOF:

Since G(0)=1/2 [probability of election outcome is 50-50 if voter buys zero votes]

voter i’s payoff when she bids zero is equal to the rebate, which is non-negative, so the

bidding mechanism is individually rational. 

END QUOTE.


Well first of all, G(0)=1/2 is not stated as an assumption and seems contradicted by 

most real world elections.   Second, even if we assume that, then I do not understand why

the fact that a voter's "payoff in non-negative if voter bids zero (i.e. does not vote)"

logically forces "the bidding mechanism is individually rational. "  ,


Huh??  I mean, essentially EVERY bidding mechnaism ever conceved of
no matter how rational/not, satisfies THAT.   So what?

Next sentence
"Moreover, for a large electorate, the central limit theorem implies that..."
is also wrong in the sense the central limit theorem is not applicable at all
unless further never-stated assumptions are true.

So:  both theorems in this Goeree-Zhang paper are 1. refuted, 2. unproven
and in both cases the theorem statement itself is simply unacceptable.

Does this mean this QVB  system is garbage?  Well, nt necessarily, I think
there is some sense in which QVB really does satisfy an optimality theorem.
I'm just saying neither the Weyl paper or this Goeree paper
ever managed to state+prove such a theorem.  I think there is a valid and good
idea here, the problem is their execution has been horrendous.


Warren D. Smith (CRV cofounder, http://RangeVoting.org)

unread,
Jun 11, 2013, 7:57:17 PM6/11/13
to electio...@googlegroups.com
Man, this just keeps getting worse and worse.

The reporter for Slate who wrote the original story on 
E.Glenn Weyl and his wonderful vote buying scheme,
it turns out was NOT just "a reporter for Slate."  
He actually was Eric Andrew Posner, a professor of law
at Univ. of Chicago.

In other words, while Posner was creating the impression for the naive reader that
he was just a random reporter covering a great scientific discovery, 
really he was a faculty colleague of E.Glenn Weyl himself (same university)
writing a self-serving puff piece promoting Weyl's work, disguised as a reporter
covering news.

I mean, is that ethical journaliism?  Normally reporters go out of their way to disclose conflicts
of interest up front, but he went the other direction (albeit I managed to figure it out,
partly by luck).

And reason I say it was "self serving" was Posner actually co-authored a different
paper with Weyl related to this topic, which is here:
and recommends use of QVB for corporate votes.
So he's actually Weyl's colleague in a very strong sense and in no way can
claim to be an unbiased reporter.

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