[EM] Dollar example
Bart Ingles
bartman at netgate.net
Wed Feb 23 13:32:30 PST 2000
I was using the term 'social utility' in the way that Merrill (1988)
appeared to be using it, so it may be incorrect from an economist's
perspective (unless the B supporters happen to be living in an area
where dollars must be exchanged at a heavy discount before they can be
spent) :-)
I don't disagree materially with the rest of Steve's comments (including
the foreign trade comment), except to point out that the candidate
vacuum argument he uses applies equally well to anti-ratings examples of
the kind:
60 A(10) B(0)
40 B(100) A(0)
As an aside, Steve appears to be calculating von Neumann-Morgenstern
utilities the way I would, except that D should probably be given a
slightly higher utility to account for the fact that it's a sure thing
-- maybe 0.6 if most voters would consider D equivalent to an AC lottery
with a 60% chance of winning. I probably should have adjusted the 0.1
utilities as well, but the difference wouldn't have mattered much.
As for the rarity of my scenarios, maybe so, but I don't think this
means that the incentive for strategic voting is necessarily rare. It
may be that in many/most elections, a substantial number of voters will
have incentive to strategize.
Bart
Steve Eppley wrote:
>
> Bart Ingles wrote:
> > This was not intended to address any particular method. Instead, this
> > deals with standards for who actually _should_ win. There was a debate
> > recently about whether the CW was always the better choice for society,
> > or whether some consideration should be given to social utility.
>
> I think most economists would look at Bart's example and say
> that all three proposals provide equal social utility ($75,000).
>
> > A community is trying to decide how best to distribute a windfall of
> > $75,500. There is a dispute over how much each member deserves. Group
> > A wants to give each of its own members $1000 for every $500 that each
> > non-member receives. Group C wants the opposite. Group B wants to give
> > each member of another group $550, and distribute the rest among its own
> > members.
> >
> > Group A and C are each close to half of the population, with group B
> > only a small minority. Exact populations are unknown.
>
> So it's unknown which is the condorcet winner. But at least one
> of them is, since the preferences can't cycle.
>
> > ~50 A($1000) B($550) C($500)
> > ~1 B($20500) A=C($500)
> > ~50 C($1000) B($550) A($500)
> >
> > Converted to vN-M utilities, we have:
> >
> > ~50 A(1.0) B(0.1) C(0)
> > ~1 B(1.0) A=C(0)
> > ~50 C(1.0) B(0.1) A(0)
> >
> > Since A and C are in a dead heat, it is clearly in those voters'
> > interest to truncate and accept the AC lottery rather than settle for
> > the $50. Note that this strategy doesn't depend on cooperation between
> > the A and C groups -- if either group votes sincerely B wins, so there
> > is no penalty for using the strategy unilaterally.
> >
> > It is hard to see how a win for B would benefit society as a whole,
> > since it mainly concentrates wealth into the hands of a small minority.
>
> It's possible that the minority would invest productively
> whereas the majority would fritter away their found money by
> buying useless toys produced abroad by a hostile nation. :-)
>
> Something Bart's recent examples haven't taken into account is
> that, given a good voting method, additional good candidates
> have an incentive to compete. What happens in this example
> if someone proposes D = "Distribute the windfall evenly" or
> D'= "Distribute the windfall evenly among groups A&C and none
> to group B"? (Why wouldn't someone in group B propose D, if
> s/he is concerned that choice B has little chance of winning?)
>
> Then choice B could not be the condorcet winner, and D or D'
> would be the condorcet winner if the A group and the C group
> are minorities.
>
> ~50 A($1000) D'~D($750) B($550) C($500)
> ~1 B($20500) D($750) A=C($500) D'($0)
> ~50 C($1000) D'~D($750) B($550) A($500)
>
> I'm not sure how to convert to "vN-M" utilities, so I'll guess
> that these are the vN-M utilities:
>
> ~50 A(1.0) D'~D(0.5) B(0.1) C(0)
> ~1 B(1.0) D(0.0366) A=C(0.0244) D'(0)
> ~50 C(1.0) D'~D(0.5) B(0.1) A(0)
>
> Since for groups A&C both choice D and choice D' are equivalent
> to the AC lottery, the A&C voters lose nothing by approving or
> ranking D and D'. Since many people are risk averse, they will
> (perhaps irrationally) prefer D with certainty more than the AC
> lottery. The B group may rank D also, if they estimate that
> choice B's chance of winning is small.
>
> I agree with Mike's comment that the scenarios Bart is concerned
> about would be rare, given a good voting method. Bart's
> examples leave a vacuum which could easily be filled by a
> good candidate, which would win and improve social utility.
>
> ---Steve (Steve Eppley seppley at alumni.caltech.edu)
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