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

Abd ul-Rahman Lomax abd at lomaxdesign.com
Mon Mar 24 10:27:51 PDT 2008

```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.

```