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<font face="Helvetica, Arial, sans-serif">I think that bringing
cardinal voting into the discussion is a red herring. <br>
My contention is as follows. Suppose that we are given a set of
ballots (eg. a set of rankings of candidates) and an adequetely
specified generative model (eg. a jury model or a spatial model).
Then there is a mathematically identifiable rightful winner (I
shall give an example in a moment). The fact that given additional
information (eg. cardinal preferences) we might prefer a different
candidate is irrelevant - it is a question of there being a valid
statistical inference from the information given. <br>
We might also consider the question of which is the best
candidate sub specie aeternitatis. This seems to me equally
irrelevant. If there exists such as thing as an objectively best
candidate, then what makes him objectively best is nothing to do
with the voters' opinions. <br>
<br>
Example of identifying the rightful winner: let the ballots come
from a Gaussian jury model. The candidates have valences (merits)
drawn from a standard univariate Gaussian, and each voter's
assessment of the valence of each candidate is a noisy estimate of
the true merit, obtained by adding an iid N(0,sigma) noise term to
the true valence. A perfect voting method will elect the candidate
whose posterior expected valence is greatest. This is a well
defined and soluble mathematical problem. <br>
<br>
CJC<br>
</font><br>
<div class="moz-cite-prefix">On 16/08/2023 17:52,
<a class="moz-txt-link-abbreviated" href="mailto:fdpk69p6uq@snkmail.com">fdpk69p6uq@snkmail.com</a> wrote:<br>
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<blockquote type="cite"
cite="mid:8285-1692204753-785806@sneakemail.com">
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<div dir="ltr" class="gmail_attr">On Mon, Aug 14, 2023 at
12:09 AM C.Benham wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
> I think this is an interesting point. We can ask at a
philosophical level what makes a good voting method. Is it
just one that ticks the most boxes, or is it one that most
reliably gets the "best" result?<br>
</blockquote>
<div><br>
</div>
<div>The one that most reliably gets the best result in the
real world. The difficulty with this approach is accurately
modeling human voting behavior and the consequent utility
experienced from the winner, but it's still the better
answer philosophically.</div>
<div><br>
</div>
<div>(Note that VSE predates Jameson Quinn by decades, and has
had several different names: <a
href="https://en.wikipedia.org/wiki/Social_utility_efficiency"
moz-do-not-send="true">https://en.wikipedia.org/wiki/Social_utility_efficiency</a>)</div>
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<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid
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> And that's partly because the premise of Condorcet is
essentially built on a logical fallacy - basically that if A
is preferred to B on more ballots that vice versa then
electing A must<br>
> be a better result than electing B.<br>
<br>
I'd be interested in reading your explanation of why you
think that is a <br>
"logical fallacy". What about if there are only two
candidates?<br>
</blockquote>
<div><br>
</div>
<div>Ranked ballots can't capture strength of preference. It's
possible for a majority-preferred candidate to be very
polarizing (loved by 51% and hated by 49%), while the
minority-preferred candidate is broadly-liked and has a much
higher overall approval/favorability rating. Which
candidate is the rightful winner?<br>
</div>
<div><br>
</div>
<div><a
href="https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html"
target="_blank" moz-do-not-send="true">https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html</a></div>
<div><br>
</div>
<div>"Suppose you and a pair of friends are looking to order a
pizza. You, and one friend, really like mushrooms, and
prefer them over all other vegetable options, but you both
also really, <i>really</i> like pepperoni. Your other
friend also really likes mushrooms, and prefers them over
all other options, but they're also vegetarian. What one
topping should you get?
<p>Clearly the answer is mushrooms, and there is no group of
friends worth calling themselves such who would conclude
otherwise. It's so obvious that it hardly seems worth
calling attention to. So why is it, that if we put this
decision up to a vote, do so many election methods, which
are otherwise seen as perfectly reasonable methods, fail?
Plurality, <a
href="http://en.wikipedia.org/wiki/Two-round_system"
target="_blank" moz-do-not-send="true">top-two runoffs</a>,
<a
href="http://en.wikipedia.org/wiki/Instant-runoff_voting"
target="_blank" moz-do-not-send="true">instant runoff
voting</a>, all variations of <a
href="http://en.wikipedia.org/wiki/Condorcet_method"
target="_blank" moz-do-not-send="true">Condorcet's
method</a>, even <a
href="http://en.wikipedia.org/wiki/Bucklin_voting"
target="_blank" moz-do-not-send="true">Bucklin voting</a>;
all of them, incorrectly, choose pepperoni."</p>
</div>
<div>(And strength of preference is clearly a real thing in
our brains. If you prefer A > B > C, and are given
the choice between Box 1, which contains B, and Box 2, which
has a 50/50 chance of containing A or C, which do you
choose? What if the probability were 1 in a million of Box
2 containing C? By varying the probability until it's
impossible to decide, you can measure the relative strength
of preference for B > C vs A > C.)<br>
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