<html><body><div style="color:#000; background-color:#fff; font-family:times new roman, new york, times, serif;font-size:12pt"><div style="RIGHT: auto"><SPAN style="RIGHT: auto">Hi Robert,</SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto">I think that the basic claim of "Condorcet doesn't necessarily pick the option whom the elecotorate prefers" (in terms of</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">total utility) won't be too controversial. Any kind of model usually assumes internal utilities (such as based on distances in</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">issue space) because we need these to figure out how voters prioritize. One could try to assume that some set of</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">internal utilities might have some absolute, aggregable value. In that case it is really easy to produce a scenario where the</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">majority favorite isn't the utility winner. All you need is one case and you get Clay's "not necessarily."</SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto">You ask how we can decide, then, not to elect voted majority favorites. Assuming voters are strategic I don't know</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">of a good answer to this.</SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto">You suggest a model where there are only two candidates and the voter-for-candidate utilities are all either 0 or 1. If </SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">that's an accurate model </SPAN><SPAN style="RIGHT: auto">then Clay's claim doesn't work. But with virtually an<VAR id=yui-ie-cursor></VAR>y other model it will be true sometimes</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">that the voted majority favorite isn't the utility maximizer.</SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Kevin</SPAN></div>
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<DIV class=hr style="BORDER-RIGHT: #ccc 1px solid; PADDING-RIGHT: 0px; BORDER-TOP: #ccc 1px solid; PADDING-LEFT: 0px; FONT-SIZE: 0px; PADDING-BOTTOM: 0px; MARGIN: 5px 0px; BORDER-LEFT: #ccc 1px solid; LINE-HEIGHT: 0; PADDING-TOP: 0px; BORDER-BOTTOM: #ccc 1px solid; HEIGHT: 0px" readonly="true" contenteditable="false"></DIV><B><SPAN style="FONT-WEIGHT: bold">De :</SPAN></B> robert bristow-johnson <rbj@audioimagination.com><BR><B><SPAN style="FONT-WEIGHT: bold">À :</SPAN></B> election-methods@lists.electorama.com <BR><B><SPAN style="FONT-WEIGHT: bold">Envoyé le :</SPAN></B> Lundi 6 février 2012 21h31<BR><B><SPAN style="FONT-WEIGHT: bold">Objet :</SPAN></B> Re: [EM] [CES #4445] Re: Looking at Condorcet<BR></FONT></DIV><BR><BR>one thing i forgot to mention...<BR><BR>On 2/5/12 5:07 PM, Kristofer Munsterhjelm wrote:<BR>> On 02/04/2012 06:14 PM, robert bristow-johnson wrote: <BR>...<BR>> that is not well defined. given Abd's
example:<BR>>> <BR>>>> 2: Pepperoni (0.61), Cheese (0.5), Mushroom (0.4)<BR>>>> 1: Cheese (0.8), Mushroom (0.7), Pepperoni (0)<BR>>> <BR>>> who says that for that 1 voter that the utility of Cheese is 0.8?<BR>> <BR>> The voter does. In this thought experiment, one simply assumes the 1-voter's utility of Cheese is 0.8 so as to show the point. The point is that there may be situations where utilitarian optimization and majority rule differs.<BR>> <BR>so my question, when running simulations or trying to construct a quantitative case of maximizing utility, it depends of course on how utility is quantitatively defined. and we understand that the aggregate utility is some combination of every voter's individual utility, and, for the sake of argument (and because it sounds reasonable), we'll say that the metric of aggregate utility is equal to the sum of the individual metrics of utility. so maximizing
the sum is the same as maximizing the mean.<BR><BR>but there is still no model of individual utility other than "one simply assumes". 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. when you guess at a model that is part of your "proof", it doesn't make for a very rigorous proof. a *real* proof is that the Devil hands you the model (that's within the domain of possible models) and you make your proof work anyway. *you* don't get to cook up heuristics like "the utility to voter X that Candidate A is elected is equal to 0.8".<BR><BR>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.<BR><BR>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?<BR><BR>sorry that i am belaboring what i would have thought were simple axioms, but i can't tell that they are widely accepted and i want to probe how they are not widely accepted. how can it be that when Candidate A gets more votes than Candidate B (and they are the only choices) that anyone would advocate awarding office to Candidate B? something has to be anomalous to come to such a conclusion. perhaps the votes for Candidate B count more than the votes for Candidate A (violating one person, one vote). perhaps we introduce a goofy rule such as tossing in a random variable (like draw two non-negative random integers within some given range and add one to Candidate A's total votes and the other to Candidate B's total votes) and Candidate B got a higher number out of the lotto.
that would make the decision threshold fuzzier, but i don't think that supporters of Candidate A would consider it fair.<BR><BR>-- <BR>r b-j <A href="mailto:rbj@audioimagination.com" ymailto="mailto:rbj@audioimagination.com">rbj@audioimagination.com</A><BR><BR>"Imagination is more important than knowledge."<BR><BR><BR><BR>----<BR>Election-Methods mailing list - see <A href="http://electorama.com/em" target=_blank>http://electorama.com/em</A> for list info<BR><BR><BR></DIV></DIV></div></body></html>