[EM] [CES #4445] Re: Looking at Condorcet

Bryan Mills bmills at alumni.cmu.edu
Tue Feb 7 23:07:19 PST 2012

On Wed, Feb 8, 2012 at 12:52 AM, <
election-methods-request at lists.electorama.com> wrote:

> Subject: Re: [EM] [CES #4445] Re: Looking at Condorcet
> Message-ID: <4F320919.8090309 at audioimagination.com>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
> On 2/7/12 6:30 PM, Juho Laatu wrote:
> > On 7.2.2012, at 5.31, robert bristow-johnson wrote:
> >
> >> how can Clay build a proof where he claims that "it's a proven
> mathematical fact that the Condorcet winner is not necessarily the option
> whom the electorate prefers"?  if he is making a utilitarian argument, he
> needs to define how the individual metrics of utility are define and that's
> just guessing.
> > Yes, I think Clay assumes that we know how the "aggregate utility" of a
> society is to be counted. There could be many opinions on how to define
> "aggregate utility" or "electorate preference", and also opinions that it
> can not be defined.
> >
> > It is actually not necessary to talk about those general concepts. It is
> enough to agree what the targets of the election are. Maybe Clay should
> tell explicitly that in this particular election that he considers the
> maximal sum of individual (sincere or given strategic) utilities to be the
> target.
> so he's seeking to maximize a measure of utility that is the sum of
> individual utilities and, again, i see no mathematical expression of the
> individual utility to sum up.  how does Clay maximize this sum of
> undefined quantities?
> as best as i can tell, we only know what this quantity of individual
> utility is for a simple two-choice election.  assuming all of the voters
> are of equal weight, if the candidate some voter has voted for is
> subsequently elected, the utility to that voter is 1.  if the other
> candidate is elected, the utility to that same voter is 0.

Your mistake is in assuming that utility is measurable by the election
system proper; it's not, and it's not intended to be.  A model supposes
that people gain in some way from candidates getting elected; that gain is
quantifiable and aggregable to an outside observer (as a property of the
model), but not by the hypothetical people being modeled.  As outside
observers, we can analyze a model by comparing the aggregate utility of
 the election result that voters within the model would produce if they
vote according to their personal utility, and comparing that to the maximum
aggregate utility of any possible election result.  (Remember, the people
within the model can't make this comparison because they have no objective
way to measure and/or aggregate utilities.)

An example might illustrate.  Suppose that in some model, if candidate A
wins, the candidate is the swing vote to pass a magical health-care plan
that extends the lives of A-supporters by 5 healthy years each without
affecting B-supporters at all.  If candidate B wins, the candidate is the
swing vote to pass a tax cut that gives all of the B-voters an extra $100
without affecting A-supporters at all.  The utility to A-supporters of A
getting elected is 5 healthy years; the utility to B-supporters is $100.
 Now suppose that the utility function in our model dictates that 5 healthy
years of lifetime is worth more than $200.  If the number of A-supporters
is more than half the number of B-supporters -- say, two-thirds --
candidate A maximizes utility; but with A = 2/3 * B, B wins any election
that satisfies the majority criterion.

So an election system that maximizes utility would *not* generally obey the
principle "one person, one vote"; it would obey a principle more like
"votes proportional to utility".  It's not possible for such a system to
exist in reality because we can't measure or compare utility -- we are
inside the "reality" model -- but we can at least look for systems that
maximize utility in models that resemble reality in certain ways.
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