[Election-Methods] YN model - simple voting model in which range optimal, others not

[Abd ul-Rahman Lomax]

At 11:21 PM 3/23/2008, Dave Ketchum wrote:
>On Sat, 22 Mar 2008 19:35:13 -0400 Warren Smith wrote:
> > The "YN model" - a simple voting model in which range voting behaves
> > optimally while many competing voting systems (including Condorcet)
> > can behave pessimally:
> >
> > http://rangevoting.org/PuzzAggreg.html
> >
>When I stare at this all I get is headaches:
>
>Why would Plurality voters be attracted to candidates with 3 Ys, or no Ys
>- yet reject 4 Ys?

Okay, candidate YYYY holds the majority position on every issue. 
However, individual voters may have different positions. The example 
given by Brams, on the site, does not spell out the voting strategy 
followed in trying this with Plurality. However, it is pretty 
obvious. As a voter, you have one of the sixteen positions, so you 
will vote sincerely for that candidate. So the table provided from 
Brams is a voting table that shows that there are this many voters 
who hold each position described. It's arbitrary, in this case, the 
example is constructed. If there are these many voters, with these 
positions, and there are none with the position YYYY, all of these 
voters will vote sincerely for a candidate other than YYYY. Q.E.D.

And that this problem seems hard shows how deeply ingrained are some 
of our habits. To directly answer Mr. Ketchum, suppose you are one of 
these voters, and your personal position on the issues involved is 
YYYN. That means that you agree with the majority on three out of 
four of the issues involved, in that order. There is a candidate with 
this exact position. So you vote for him or her. In the example, only 
three other voters are exactly like you. No voters vote for YYYY 
because, in this example, no voters have that exact position, and 
because every position is represented in this 16-candidate election, 
they all have another candidate whom they prefer. If you look at each 
issue position in the chart, you will see that a majority of voters 
would approve of each "motion" if presented individually. (I have not 
verified this, but if it isn't so, a serious mistake was made either 
in the model or in presenting it.)

>Why would Condorcet voters seem to be attracted to Ns?  If the answer is
>that they truly are, why should Condorcet be blamed as if a bad method?

Read the thing again. The chart is a table of positions in the 
electorate, which then, by the terms of the problem, can be used to 
predict votes. With Range, an assumption was made that you would vote 
according to how much you agreed with the candidate. Apparently all 
issues were considered equally important. With Plurality, you would 
vote for your favorite only, which is simple, because there is 
exactly one such candidate, there being only one candidate holding 
each exact position.

The question about Condorcet winners being "attracted" to Ns shows 
that the point has been entirely missed. Voters are attracted to 
candidates who agree with them. If your position on an issue was, for 
example, NNNN, you would vote for that candidate. Voters are not 
"Condorcet voters," rather, a Condorcet method takes a ranked ballot 
and translates in a certain way, IRV translates it differently, Borda 
differently, etc. In any case, to study how a ranked method will 
apply to this situation, we simply assume that each voter votes first 
rank for the candidate with an exact match to the voter's position. 
The voter is going to have exact agreement with no other candidates. 
This is enough, first of all, to tell us that YYYY will not win under 
IRV, because all lower rankings will be moot, that candidate is the 
first one eliminated. "Core support" criterion, that lovely creation 
of Rob Richie, requires this as if it were desirable, when this 
example shows a case where a representative -- say it is a rep being 
elected -- agrees with the electorate majority on every issue, 
possibly, cannot win. Is this a common case? That is not asserted; 
for starters, the 16-candidate field is pretty unusual. Except in San 
Francisco.

So we eliminate, for the individual voter, the exact match candidate. 
We now have a choice of candidates who agree with the voter on three 
out of four issues. The problem, you will note, isn't solved on that 
web page. We could make a nice neat assumption that somehow these 
issues have been arranged in a universal sequence of importance, so 
that agreement in the first position is more important than that in 
second, and so on. The effect is that the fourth issue is dropped, 
there are now eight unique positions, each held by two candidates; 
one of these, however, was in first rank, so the other one is now the 
second choice. And, by recursion, we can determine the vote of each 
voter. I haven't done it. Once upon a time, I would have. Life moves on.