I'm sure you're aware that the Anglo-American Analytical philosophical perspective of Utilitarianism is not highly esteemed among philosophers.<div><br></div><div>One reason is that the presumption of Cardinal Utility implicit with Bayesian Regret analyses is a strong one. </div>
<div>Let's say we treat voter utilities as Ordinal instead. In that case, one can perform any monotonically positive transformation on the utilities and </div><div>it would keep the relative rankings of all of the candidates. </div>
<div>Let's say Xij is a voter i's utility for candidate j on a continuous scale of 0-10. </div><div>Then, let's say ci is some randomly generated value from 0-infinity, perhaps from a log-normal distribution.</div>
<div><br></div><div>We could then transform Xij into Yij by having Yij=Xij^ci * 10^(1-ci). </div><div><br></div><div>If one proceeds to determine votes based on Yij, but evaluate the votes based on Xij</div><div><br></div>
<div>then by construction approval or range voting would not perform as well, but those election rules based only on rankings would perform the same as before. </div><div><br></div><div>So it seems to me that the choice between rank-based and approval/range/mj election rules depends on whether voter utility for candidates is better understood as ordinal or cardinal, </div>
<div><br></div><div>or perhaps it's a mix of both plus a haze from the plethora of misinformation and manipulations of their fears....</div><div><br></div><div>At any rate, this is why I've argued that ascertaining the best single-winner election rule is nowhere near as important as pitching the importance of mixing the use of single-winner and multi-winner election rules, with the latter replacing the former more so in "more local" elections that are not competitive often in single-winner elections. </div>
<div>dlw</div><div><br><div class="gmail_quote">On Tue, Feb 7, 2012 at 11:52 PM, <span dir="ltr"><<a href="mailto:election-methods-request@lists.electorama.com">election-methods-request@lists.electorama.com</a>></span> wrote:<br>
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<br>Today's Topics:<br>
<br>
1. Re: [CES #4445] Re: Looking at Condorcet (Juho Laatu)<br>
2. Re: Kristofer: MJ & RV (Jameson Quinn)<br>
3. Re: [CES #4445] Re: Looking at Condorcet (robert bristow-johnson)<br>
4. Re: [CES #4445] Re: Looking at Condorcet (robert bristow-johnson)<br>
<br><br>---------- Forwarded message ----------<br>From: Juho Laatu <<a href="mailto:juho4880@yahoo.co.uk">juho4880@yahoo.co.uk</a>><br>To: EM list <<a href="mailto:election-methods@lists.electorama.com">election-methods@lists.electorama.com</a>><br>
Cc: <br>Date: Wed, 8 Feb 2012 01:30:33 +0200<br>Subject: Re: [EM] [CES #4445] Re: Looking at Condorcet<br>On 7.2.2012, at 5.31, robert bristow-johnson wrote:<br>
<br>
> 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.<br>
<br>
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.<br>
<br>
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.<br>
<br>
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.)<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>
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.<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>
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.<br>
<br>
Juho<br>
<br>
<br>
<br>
<br>
<br><br>---------- Forwarded message ----------<br>From: Jameson Quinn <<a href="mailto:jameson.quinn@gmail.com">jameson.quinn@gmail.com</a>><br>To: MIKE OSSIPOFF <<a href="mailto:nkklrp@hotmail.com">nkklrp@hotmail.com</a>><br>
Cc: <a href="mailto:election-methods@electorama.com">election-methods@electorama.com</a><br>Date: Tue, 7 Feb 2012 17:19:56 -0600<br>Subject: Re: [EM] Kristofer: MJ & RV<br><br><br><div class="gmail_quote">2012/2/7 MIKE OSSIPOFF <span dir="ltr"><<a href="mailto:nkklrp@hotmail.com" target="_blank">nkklrp@hotmail.com</a>></span><br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div><div dir="ltr">
Kristofer:<br><br>You say that MJ and RV are the methods to propose because they're the ones that meet the two criteria you defined.<br><br>Have you demonstrated that they're the only ones?<br><br>What about Approval? It's simpler. Simpler to define, implement and vote. And supplementable by the conditionality options that I've<br>
described, to get rid of the co-operation/defection problem.<br><br>Your reply regarding MJ seemed basically to be saying that maybe you won't regret voting sincerely in MJ. That's great if you like "maybe".<br>
<br>When you say that some will rate sincerely, you're moving the topic to psychology. And I like the way you guys like to theorize about how people<br>would vote, while declining to find out what voting is like in the various proposed methods, via a poll.<br>
</div></div></blockquote><div><br></div><div>I am engaged in exactly this research through mturk. I will let the list know when I have worthwhile results.</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div><div dir="ltr"><br>But maybe you're right. Maybe in MJ some would rate sincerely and some would, instead, voting in their best interest.<br><br>Whether that is good or bad depends on whether the suckers are your co-factionalists or mine.</div>
</div></blockquote><div><br></div><div>In the chicken dilemma, "suckers" tend to be good for the society as a whole. </div><div><br></div><div>Jameson</div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div><div dir="ltr"><span><font color="#888888"><br><br>Mike Ossipoff<br> </font></span></div></div>
<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></blockquote></div><br>
<br><br>---------- Forwarded message ----------<br>From: robert bristow-johnson <<a href="mailto:rbj@audioimagination.com">rbj@audioimagination.com</a>><br>To: <a href="mailto:election-methods@lists.electorama.com">election-methods@lists.electorama.com</a><br>
Cc: <br>Date: Wed, 08 Feb 2012 00:33:13 -0500<br>Subject: Re: [EM] [CES #4445] Re: Looking at Condorcet<br>On 2/7/12 6:30 PM, Juho Laatu wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
On 7.2.2012, at 5.31, robert bristow-johnson wrote:<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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.<br>
</blockquote>
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.<br>
<br>
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.<br>
</blockquote>
<br>
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?<br>
<br>
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.<br>
<br>
but when there is a multi-candidate race, this is much more poorly defined. say there are 3 candidates, if the candidate that some voter votes for is elected, the measure of utility (to that voter) is 1. if the candidate that this voter ranked last is elected, the utility to that voter is 0. but what about that voter's 2nd choice? it depends who it is and who it is to the voter. if we were to always assume that the utility is 1/2, then it seems like the kind of assumption Borda makes. but the voter's 1st and 2nd choice could be very close to each other, or the 2nd choice could be a piece of crap just a little better than the last choice. we don't know. so how do you put together an argument that "it's a proven mathematical fact that the Condorcet winner is not necessarily the option whom the electorate prefers" when you just don't know whom the electorate prefers because you don't know the utility metrics for each voter?<br>
<br>
if you answer, "we ask the voters what the utility measure is with a Score ballot", then my response is: "how do you know that this is accurate? that the voter even knows or that the voter isn't lying on his ballot to try to bury his 2nd choice or to compromise and forsake his favorite candidate?" there are so many assumptions made here, it's like we're pulling numbers out of our butts.<br>
<br>
hardly constitutes anything approximating "a proven mathematical fact".<br>
<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
And then he could continue to say that Condorcet is not designed to meet this target.<br>
</blockquote>
<br>
how does he know when this target is not even operationally defined.<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Condorcet may however perform quite well as a method that approxmates that target in a highly competitive environment.<br>
<br>
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.)<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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>
</blockquote>
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.<br>
</blockquote>
<br>
what other conditions could be agreed on? Two-candidate is a given, High stakes and Competitive are pretty hard to agree to change, they are just there. if you want to consider a variance to Equal franchise, then whose ballots are going to be attenuated? will you be able to get those voters to agree to have their ballots each count less than your ballot?<br>
<br>
this is soooo fundamental. all i want to do is get people to agree that when there are only two choices, that the candidate with the most votes wins, which is simple enough. if you *don't* agree with this, what are the conditions you are envisioning for when election to office is awarded to the candidate with the fewest votes? sometimes when considering a simplified case like this, you have to ask yourself about the contra-indication. either you award the election to the candidate with the greater number of voters or you award the election to the candidate with the fewer number of votes. i am astonished that anyone can see this in any more nuanced manner. how would you *ever* award election to the less-supported candidate?<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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>
</blockquote>
I think he made his assumptions / definition of the general utility of the society<br>
</blockquote>
<br>
and what are they? general utility of the society is equal to the sum of the individual utilities, so how are the individual utilities defined? i don't see an answer there and i don't see how there *can* be an answer without making a lot of assumptions. and then if you do that, i don't see much confidence in the answer arrived at.<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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.<br>
</blockquote>
<br>
if it's not the majority that rule, what's the alternative?<br>
<br>
once we can settle this simple issue, i'll move on to "why Condorcet".<br>
<br>
-- <br>
<br>
r b-j <a href="mailto:rbj@audioimagination.com" target="_blank">rbj@audioimagination.com</a><br>
<br>
"Imagination is more important than knowledge."<br>
<br>
<br>
<br>
<br>
<br>
<br><br>---------- Forwarded message ----------<br>From: robert bristow-johnson <<a href="mailto:rbj@audioimagination.com">rbj@audioimagination.com</a>><br>To: <a href="mailto:election-methods@lists.electorama.com">election-methods@lists.electorama.com</a><br>
Cc: <br>Date: Wed, 08 Feb 2012 00:51:55 -0500<br>Subject: Re: [EM] [CES #4445] Re: Looking at Condorcet<br>On 2/7/12 2:07 PM, Kevin Venzke wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Hi Robert,<br>
I think that the basic claim of "Condorcet doesn't necessarily pick the option whom the elecotorate prefers" (in terms of<br>
total utility) won't be too controversial. Any kind of model usually assumes internal utilities (such as based on distances in<br>
issue space) because we need these to figure out how voters prioritize. One could try to assume that some set of<br>
internal utilities might have some absolute, aggregable value. In that case it is really easy to produce a scenario where the<br>
majority favorite isn't the utility winner.<br>
</blockquote>
<br>
in the two-candidate case, you would have to assume unequal treatment for voters. if all voters' votes have equal weight, you must accept that the majority candidate is also the choice maximum general utility to the society that the voters come from.<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
All you need is one case and you get Clay's "not necessarily."<br>
</blockquote>
<br>
sure, but attaching "not necessarily" to "proven mathematical fact" is a pretty meaningless semantic. the proven mathematical fact says essentially nothing. like a tautology.<br>
<br>
but when Clay says that Score or Approval is better at picking the Condorcet winner than is a Condorcet-compliant method, *that* is no tautology is obviously controversial, since it says that there is a number closer to 3 than the number 3 itself.<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
You ask how we can decide, then, not to elect voted majority favorites. Assuming voters are strategic I don't know of a good answer to this.<br>
You suggest a model where there are only two candidates and the voter-for-candidate utilities are all either 0 or 1.<br>
</blockquote>
<br>
if it isn't 0 (for when you don't get who you voted for) and 1 (for when your candidate is elected), then some voter is diluting their utilities and i think it's pretty useless and in bad taste to ask voters to do that explicitly with a Score ballot.<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
If that's an accurate model then Clay's claim doesn't work. But with virtually any other model it will be true sometimes<br>
that the voted majority favorite isn't the utility maximizer.<br>
</blockquote>
<br>
well, once we get three or more candidates, it's a question as to whom either the "majority favorite" is or who is the "utility maximizer."<br>
<br>
Condorcet doesn't go there. Condorcet makes no other assumptions other than the "simple majority" and "one person, one vote" (which are what we already base two-choice elections on) when any two candidates are paired up. and then Condorcet imposes logical consistency: If Candidate A is the best choice for office, then Candidate A must be a better choice than Candidate B. And Candidate A must be a better choice than Candidate C. etc.<br>
<br>
-- <br>
<br>
r b-j <a href="mailto:rbj@audioimagination.com" target="_blank">rbj@audioimagination.com</a><br>
<br>
"Imagination is more important than knowledge."<br>
<br>
<br>
<br>
<br>
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