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I've added a chapter on Condorcet method to my book on FAB STV: Four
Averages Binomial Single Transferable Vote, published last week.<br>
From<br>
Richard Lung.<br>
<br>
On 29/03/2018 09:03, robert bristow-johnson wrote:
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cite="mid:5d9562fb3d2cf49d2b0066660cdbb2e0.squirrel@webmail04.register.com"
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<p><br>
<br>
---------------------------- Original Message
----------------------------<br>
Subject: [EM] "Condorcet winner" versus "winner of Condorcet's
method" (was Re: 2018 Chess Candidates Tournament)<br>
From: "Steve Eppley" <a class="moz-txt-link-rfc2396E" href="mailto:SEppley@alumni.caltech.edu"><SEppley@alumni.caltech.edu></a><br>
Date: Wed, March 28, 2018 11:52 am<br>
To: <a class="moz-txt-link-abbreviated" href="mailto:election-methods@lists.electorama.com">election-methods@lists.electorama.com</a><br>
--------------------------------------------------------------------------<br>
<br>
> @Ross Hyman: Ding Liren was not a Condorcet<br>
> winner in that chess tournament, because a<br>
> Condorcet winner is an alternative that<br>
> defeats all other alternatives pairwise. <br>
> Ding Liren didn't defeat all other players;<br>
> he won only one game.</p>
<p>yes, i would not call that the CW.</p>
<p><br>
> Some people might prefer a weaker,<br>
> non-standard definition of Condorcet winner:<br>
> a candidate that's undefeated pairwise. (Like<br>
> Ding Liren.) In public elections the two<br>
> definitions (if implemented by two voting<br>
> methods) would behave the same with regard to<br>
> the incentives on candidates, potential<br>
> candidates, voters, parties, donors, etc.,<br>
> because ties are rare when there are many<br>
> voters, as there are in public elections.<br>
</p>
<p>and the reason for that is that with an electorate of decent
size (like at least hundreds of voters) the probability of a tie
in any pairing of candidates is very low.</p>
<p><br>
> Don't be misled the way many people have<br>
> been, especially mathematicians not familiar<br>
> with the social choice theory literature. <br>
> They wrongly believe "Condorcet winner" means<br>
> the winner according to Condorcet's method,<br>
> and thus that Condorcet's method simply<br>
> elects the candidate that defeats all others<br>
> pairwise, and is indecisive when no such<br>
> candidate exists. "Condorcet winner" is a<br>
> term of art (a.k.a. jargon). Unlike Borda<br>
> winner, which is not a term of art and merely<br>
> means the winner according to Borda's method,<br>
> and Black's method, which is not a term of<br>
> art and merely means the winner according to<br>
> Black's method, etc.<br>
><br>
> Because sometimes there is no candidate that<br>
> defeats all others pairwise, the confusion<br>
> has caused a number of writers to wrongly<br>
> claim Condorcet's method is often indecisive<br>
> and therefore unsuitable for elections.</p>
<p>i just read what i see here and what i see in the EM wiki and
in Wikipedia. i hadn't thunk there was a "Condorcet's method"
but that there are a few decisive methods that are "Condorcet
compliant", which means these methods
will elect the CW **if** a CW exists (and i really think that in
most public elections with a ranked-order ballot, that a CW will
exist virtually all of the time, and most of the time, i'll bet
that the IRV method will also elect the CW, but not always).</p>
<p>> (In simulations with random
voting, the frequency<br>
> of scenarios in which no candidate defeats<br>
> all others increases asymptotically to 100%<br>
> as the number of candidates increases to<br>
> infinity, and as the number of voters<br>
> increases.) But the voting method Condorcet<br>
> promoted in his famous 1785 essay is very<br>
> decisive:<br>
><br>
> CONDORCET'S METHOD (copied from page lxviii<br>
> of his 1785 essay):<br>
><br>
> Here's its literal translation to English:<br>
> "The result of all the reflections that we<br>
> have just done,<br>
> is this general rule, for all the times when<br>
> one is forced to elect:<br>
> one must take successively all the<br>
> propositions that have<br>
> the plurality, commencing with those that<br>
> have the largest,<br>
> and pronounce the result that forms from<br>
> these first<br>
> propositions, as soon as they form it,<br>
> without regard<br>
> for the less probable propositions that<br>
> follow them."<br>
><br>
> The phrase "this general rule, for all the<br>
> times when one is forced to elect" meant he<br>
> was referring to a very decisive voting method.<br>
><br>
> A "proposition" is a pairwise statement like<br>
> "x should finish ahead of y." It has the<br>
> plurality if the number of voters who agree<br>
> with it exceeds the number of voters who<br>
> agree with the opposite proposition.<br>
><br>
> "Taking successively commencing with the<br>
> largest" means considering the propositions<br>
> one at a time, from largest to smallest.<br>
> (Like MAM and Tideman's Ranked Pairs do. <br>
> However, MAM and Ranked Pairs measure size in<br>
> different ways: MAM measures the size of the<br>
> majority, whereas Ranked Pairs subtracts the<br>
> size of the opposing minority from the size<br>
> of the majority.<br>
</p>
<p>that's RP-margins. there is also RP-winningVotes. how does
this method from Condorcet differ from RP-winningVotes?</p>
<p><br>
> The word "plurality" can<br>
> mean either of those: either the larger<br>
> count, or the difference between the larger<br>
> count and the opposing count.)<br>
><br>
> The "result" is an order of finish, like "x<br>
> finishes ahead of y, y finishes ahead of z,<br>
> etc." It's a collection of pairwise results,<br>
> each of which is obtained either directly<br>
> from a proposition that has a plurality, or<br>
> transitively from a combination of pairwise<br>
> results obtained directly. An example of a<br>
> pairwise result obtained transitively is the<br>
> pairwise result "x finishes ahead of z"<br>
> obtained transitively from "x finishes ahead<br>
> of y" and "y finishes ahead of z." By<br>
> definition, an order of finish is an<br>
> ordering, and is thus transitive and acyclic.<br>
><br>
> "Without regard for the less probable<br>
> propositions that follow" means disregarding<br>
> propositions that conflict (cycle) with the<br>
> results already obtained from propositions<br>
> that have larger pluralities.</p>
<p>I cannot see how that differs from Ranked Pairs.</p>
<p><br>
> For example,<br>
> disregarding "z should finish ahead of x"<br>
> after having obtained the pairwise results<br>
> that "x finishes ahead of y" and "y finishes<br>
> ahead of z."<br>
><br>
> Note: No language in the definition of<br>
> Condorcet's method refers to an alternative<br>
> that defeats all others pairwise. (Nor to an<br>
> alternative that's undefeated pairwise.) <br>
> Although it can be deduced that Condorcet's<br>
> method will elect an alternative that defeats<br>
> all others, it will also elect an alternative<br>
> even when no alternative defeats all<br>
> others... in other words it's very decisive. </p>
<p>so this historical "Condorcet's method" always elects a
single-winner and, **if** a pairwise champion exists, it will
elect that pairwise champion. so "Condorcet's method" is
Condorcet-compliant.</p>
<p><br>
> People who write about "Condorcet completion"<br>
> rules -- first check whether there exists an<br>
> alternative that defeats all others and then,<br>
> if no such alternative exists, proceed in<br>
> some other way to find the winner -- have<br>
> misunderstood Condorcet's method,<br>
</p>
<p>or, perhaps we haven't heard of Condorcet's "method". but if
they apply "Condorcet completion" rules to another
Condorcet-compliant method that doesn't need completion rules
(such as RP or Schulze), i think that reflects the same
misunderstanding.</p>
<p><br>
> which is<br>
> already "complete" (very decisive when there<br>
> are many voters, because when there are many<br>
> voters it's rare that any two majorities are<br>
> the same size, and rare that any pairings are<br>
> ties).</p>
<p>yup.</p>
<p>thanks for the information, Steve.</p>
<p><br>
--<br>
<br>
r b-j <a class="moz-txt-link-abbreviated" href="mailto:rbj@audioimagination.com">rbj@audioimagination.com</a><br>
<br>
"Imagination is more important than knowledge."<br>
</p>
<p> </p>
<p> </p>
<p> </p>
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