[EM] Remember Toby

[Juho Laatu]

On 28.5.2011, at 23.16, robert bristow-johnson wrote:

> 
> On May 28, 2011, at 3:41 PM, S Sosnick wrote:
> 
>> 
>> On 27-May-2011, Jameson Quinn, wrote, "I agree [with Juho Laatu].  If minimax is twice as likely
>> to be adopted, because it's simpler, and gives >95% of the advantage vs. plurality of the
>> theoretically-best Condorcet methods, then it *is* the best.  And besides, if we try to get
>> consensus on which is the absolutely best completion method, then almost by
>> definition, we're going to end up arguing in circles (cycles?)."
>> 
>> I also agree.  More noteworthy, however, is that Nicolaus Tideman does, too.  At page 242 of
>> "Collective Decisions and Voting" (2006), he says, "If voters and vote counters have only a slight
>> tolerance for complexity, the maximin rule is the one they would reasonably choose."
> 
> will minimax of margins decide differently than ranked pairs?  if the cycle has only three candidates, it seems to me that it must be equivalent to ranked pairs.

With cycles of three maybe the main difference between the most popular methods is the choice between margins and winning votes. In addition to that minmax may elect outside the top cycle in the rare case that the defeats within the top cycle are all stronger than any of the losses of some candidate outside the top cycle.

> 
> is there any good reason to use minimax of winning votes (clipped at zero) over minimax using margins?

I guess the usual arguments on e.g. strategic voting and strength of pairwise comparisons apply on this comparison in both directions. If one looks for simplicity and ease of explaining the method and ease of following the vote counting process, then margins has some advantages since, as said, it always measures the number of additional (first preference) votes each candidate would have needed (or would still need) to beat all other candidates.

>  it seems to me that a candidate pairing where Candidate A just squeaks by Candidate B, but where a lotta people vote should have less weight than a pairing where one candidate creams the other, but fewer voters weighed in on it.

In margins pairwise victory of 55-45 is as strong as 35-25. In winning votes 55-45 is as strong as 55-5. In the margins example 35 is not a majority but it is 40% bigger than 25 (while 55 is only 22% bigger than 45). In the winning votes example both victories have majority but in the latter one the winning side has more than ten times the number of votes of the other side. It is hard to say what kind of a rule would be ideal for all elections. Minmax(margins) in a way relies on the "required additional voters" philosophy when measuring the strength of preferences. (There are also other approaches to measuring the pairwise preferences, like counting the proportion, e.g. 55/45 = 122%.)

Juho


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