[EM] "Market based voting" paradigm. Revolutionary(?) design idea for multiwinner election schemes.

[Warren Smith]

> In your case, the buyers are the voters. They bid using an account of
> pseudo-money. However, who are the sellers?

--there are none, or it doesn't matter.

> In your Vickrey example, it
> doesn't matter, because the buyers' desiderata are the only thing we
> care about

--exactly.

> However, if we're to turn to more general auctions,
> then it may become a problem.

--huh?

> For instance, consider an auction with a reservation price. In ordinary
> auctions, the sellers set that price; but in the voting equivalent, I
> can't see who the sellers would be (the candidates? Candidate withdrawal
> option? 36.9 ultimatum?).

--I don't see why anybody would want to "set a reservation price."
There is no seller.
Why should anybody care?

> You might say, so what? Just focus on the buyers' desiderata. But then
> we might overlook solutions that don't exist as auctions because the
> sellers would never agree to them;

--so what?  There are no sellers.

> and conversely, some auctions or
> other bargaining methods may be unsuited to voting methods because the
> sellers (whoever they are) are part of it, such as with determining a
> reserve price.

--??

> Rather than consider the methods auctions, it might be better to
> consider them general markets, ... the money is not really money, and so
> there's little point in minimizing it except for that it gives you more
> freedom in the end (if more money buys a greater chance of having a seat).

--well.   Why is money worth anything in the usual economy?  Why do we
try to pay less for items we want?  Answer: so we can have more money
left over to use for later purchases of other stuff.   If however you
were soon going to die and hence soon would be unable to "make later
purchases of other stuff" you would not care about saving your money.

Similarly, in the voting situation, the only reason people have to
vote honestly and not overbid/exaggerate, is they want to have money
left over for later seat "purchases."   If it were a single winner
election, or if we were electing the last seat, they would no longer
care about that.   That is why I wanted this system to (a) be only for
MULTIwinner elections, and (b) voters must specify all votes=bids
BEFORE any seats won (and then have to stay with those same bids
forever).  This was intended to make money be "meaningful" to
maximally-incentivize voter honesty.

It seems to me the real criticism of this method, if there is one,
must focus on the fact
my "buyers" are not individuals but rather loose collectives.   That
alters the dynamics in
the voting world versus in the economo-world.  Perhaps in a bad way.
It also offers some freedom for changing the rules/formulas to
overcome whatever problems this introduces (if we understood what they
were).

------

Perhaps it will help to give this example (been discussing this at the
election science foundation googlegroup): suppose there are some
fractions of red and blue voters.
How should they vote?

I think a somewhat rough guess at the answer is:
as a voter,
1. estimate how many seats N your-color can hope to win (e.g. if reds are 40%
of the population, they could hope to win about 40% of the seats).
2. bid about $1000/N for each red candidate.

Some reasoning behind that:
If there are W winners, the "price of a seat" is (per voter)  about $1000/W
by the "law of supply and demand."  (Money supply = V*1000 if V voters;
demand = W seats in all, so estimated price of seat is V*1000/W, and
per voter is 1000/W.)
If the reds are fraction F of the population they need to bid about $1000/(W*F)
in order to collectively bid high enough to win seats at this "market price."
If they do so, they will win about W*F seats then run out of money.
If somebody else bids way higher than market price, they'll win the
first seat but
overall get fewer seats because they'll run out of money too soon, so
it was a bad voting strategy.
If somebody bids way lower than market price, they won't win seats, so that also
was a bad strategy.  The best strategy is roughly "honesty" i.e.
market price bids.
if you bid slightly too low or high it won't matter too much because
every time you
lose or win an auction your money gets rescaled up or down with
respect to the other
voters so you kind of get automatic corrections for your mis-estimations.

However, actually, the red vs blue scenario can be thought of
apparently exactly as a 2-player Von Neumann matrix game ("moves" by
the red or blue player are "determine how much to bid" and "payoff" is
#seats won) and the best strategy is well known to be "mixed" in
general, i.e. a RANDOMIZED strategy where the red bid is some random
number, etc.  However, presumably the probability distribution of
these random numbers is peaked near the market price estimate I said.

-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
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and
math.temple.edu/~wds/homepage/works.html