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

[Juho Laatu]

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 "aggergate 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. And then he could continue to say that Condorcet is not designed to meet this target. Condorcet may however perform quite well as a method that approxmates that target in a highly competitive environment.

For some other election the target could be to let the majority decide, or to maximize the worst outcome to any individual voter. Clay's target (corrected to refer to the sum of preferences based target of the election, not to the ambiguous electorate preference) may thus be valid for some elections but not all. (Also Range could be used to approximate majority decisions or Condorcet criterion, but only approximate.)

> now, with the simple two-candidate or two-choice election that is (remember all those conditions i attached?) Governmental with reasonably high stakes, Competitive, and  Equality of franchise, you *do* have a reasonable assumption of what the individual metric of utility is for a voter.  if the candidate that some voter supports is elected, the utility to that voter is 1.  if the other candidate is elected, the utility to that voter is 0.  (it could be any two numbers as long as the utility of electing my candidate exceeds the utility of not electing who i voted for.  it's a linear and monotonic mapping that changes nothing.)  all voters have equal franchise, which means that the utility of each voter has equal weight in combining into an overall utility for the electorate.  that simply means that the maximum utility is obtained by electing the candidate who had the most votes which, because there are only two candidates, is also the majority candidate.

I wouldn't say that "the maximum utility is obtained" because that is a too much general utility oriented term. I'd say that "the maximum utility to the society, as agreed, is obtained". Or maybe "the most reasonable practical result is obtained" (based on the conditions that you gave). I thus want to see also your conditions as one possible agreed way to define the (in this case maybe only sensible) targets for the election.

> if Clay or any others are disputing that electing the majority candidate (as opposed to electing the minority candidate) does not maximize the utility, can you please spell out the model and the assumptions you are making to get to your conclusion?

I think he made his assumptions / definition of the general utility of the society and then assumed that this can be set as an universal target also for all single-winner elections. I wouldn't generalize that approach that much. For example majority oriented elections are a common practice in most societies. So we have at least two fundamentally different approaches to defining the targets of an election. For competitive environments I find your approach to be a very sensible approach. You can either assume that majority rule is what you want, or that majority rule is what you must satisfy with in a competitive environment.

Juho