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<font face="Helvetica, Arial, sans-serif">Well Joe, my response is
less enthusiastic than Forest's. I think you should purge your
mind of anything you've learnt from Arrow. What's missing from
your account (and from Arrow's theorem) is any reference to truth:
you don't ask which is the right answer, or what makes it right,
or whether the discrepancies are due to bad luck or to the
unreliability of the voting methods.<br>
This is not to say that the right answer can be seen by
inspection - it depends on context. In my view, if the ballots are
rankings in a figure-skating competition, then the Borda winner is
probably right, and if they are rankings in a referendum for
minimum driving age, then the Condorcet winner is almost certainly
right. There are harder examples in which different Condorcet
methods give different results. The contextual information needed
to identify the rightful winner then becomes highly specific, and
the task of recognising the rightful winner almost impossible. If
you see the problem in terms of the relationship between voting
methods and truth, then it is hard but intelligible, while if you
see it as a collision between arbitrary voting methods and
arbitrary principles, then it is fertile in nothing but paradox. <br>
You've given me a pretext to jump on my favourite soap box...
so I stop here. <br>
CJC<br>
</font><br>
<div class="moz-cite-prefix">On 11/09/2022 18:00, Joe Malkevitch
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:fd3b89c1e5194392891b0d219a466905@york.cuny.edu">
<pre class="moz-quote-pre" wrap="">Hi:
This post is a reaction to recent list discussions.
The election below (highest rank at the left) shows the votes of 55 voters who produced ballots without ties or truncation, putting to the side if ballot rules allowed indifference or truncation. I designed this example for students in various mathematics courses that included some attention to mathematical modeling to explore the notion of the will of the voters.
The method used to decide the election matters for the result.
18 votes ADECB
12 votes BEDCA
10 votes CBEDA
9 votes DCEBA
4 votes EBDCA
2 votes ECDBA
If you use the ballots to choose a single candidate to win using:
Plurality
Run-off between two candidates with largest number of first place votes
Sequential run-off (IRV)
Borda
Condorcet (Select candidate who can beat all others in a 2-way race if there is one)
You discover the he 5 methods yield 5 different winners!
The backdrop for this example (and others in its spirit) are the theorems of Arrow, Satterthwaite and others that relate election methods to “desirable and fairness” properties.
It also relates to the issue of the skills real world voters can provide via “honest” ballots and how one should design elections which involves the choice of ballot type and the system used to count the ballots. There is also the issue of how the voters get information about the candidates and use this information to fill out there ballots. Polls whose accuracy is hard to be sure of often seem to be more important in how some voters vote rather than what the candidates stand for. What one does also depends on what “objective function” is being used.
Regards,
Joe
------------------------------------------------
Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
My email is:
<a class="moz-txt-link-abbreviated" href="mailto:jmalkevitch@york.cuny.edu">jmalkevitch@york.cuny.edu</a>
web page:
<a class="moz-txt-link-freetext" href="http://york.cuny.edu/~malk/">http://york.cuny.edu/~malk/</a>
----
Election-Methods mailing list - see <a class="moz-txt-link-freetext" href="https://electorama.com/em">https://electorama.com/em</a> for list info
</pre>
</blockquote>
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