<div dir="auto"><div>Kristofer noted in passing a very important and under-appreciated advantage of Condorcet methods:<div dir="auto"><br></div><div dir="auto"><span style="font-family:sans-serif;font-size:12.8px">It can be shown that, for methods where a majority can always force an </span><span style="font-family:sans-serif;font-size:12.8px">outcome by coordinating how they vote, then modifying the method so that it</span><span style="font-family:sans-serif;font-size:12.8px"> elects the Condorcet winner if there is one never increases the </span><span style="font-family:sans-serif;font-size:12.8px">proportion of elections where strategy is useful, and may indeed reduce it.</span><br></div><div dir="auto"><br></div>This is a good reason to routinely include in the description of every Universal Domain single winner method that satisfies the Majority Criterion, verbiage to the effect ...</div><div dir="auto"><br></div><div dir="auto">"Lacking a candidate that outranks any opponent on more ballots than not ..."</div><div dir="auto"><br></div><div dir="auto">-Forest</div><div dir="auto"><br><div class="gmail_quote" dir="auto"><div dir="ltr" class="gmail_attr">El sáb., 28 de may. de 2022 9:43 a. m., Kristofer Munsterhjelm <<a href="mailto:km_elmet@t-online.de">km_elmet@t-online.de</a>> escribió:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">On 24.05.2022 21:05, Richard Lung wrote:<br>
> <br>
> The snag is that these and other criteria were invented for what<br>
> amounts to uninomial elections, that is elections that don't have both,<br>
> or either, a rational election count and a rational exclusion count.<br>
> Together they make possible the application of the binomial theorem, to<br>
> higher order counts. My binomial STV hand count is just a first order<br>
> binomial count of one election count and one exclusion count. <br>
<br>
The criteria are method-agnostic: for any ranked voting method (in this<br>
case, that supports truncation), if someone gives you a failure example,<br>
you can verify if the method passes or fails the criterion without<br>
knowing anything about the internals of the method.<br>
<br>
Put differently, suppose that in a scenario perhaps reminiscent of<br>
Roadside Picnic, a mysterious device falls out of the sky. And it turns<br>
out that this mysterious device calls elections: you can input ranked<br>
ballots with a set of buttons and get the results shown as a series of<br>
lights on the other end.<br>
<br>
Then as long as it allows for ballots with truncation, it's possible to<br>
check if a particular ballot where A-first voters truncate can be used<br>
to induce a later-no-harm failure.<br>
<br>
Whether the strange technology that makes up the device implements<br>
rational election and exclusion counts doesn't matter. As long as it's a<br>
ranked voting method outputting winners and supporting truncation, the<br>
question "does this pass later-no-harm?" makes sense.<br>
<br>
The same goes for things like monotonicity, participation, consistency,<br>
Smith, Condorcet, etc. The criteria say something about the desired<br>
behavior of a method. Nothing about the inner workings makes the<br>
criteria inapplicable (apart from some exceptions like the polynomial<br>
runtime criterion).<br>
<br>
Without a mathematical description of the method, you couldn't be sure<br>
it actually passes later-no-harm or later-no-help, but as soon as you<br>
found a counterexample, that would settle the question in the negative.<br>
<br>
> I am not aware of any untoward effects of tactical voting on the bstv<br>
> system. I am aware of it doing away with residual irrationalities to<br>
> traditional stv, including Meek method. Tho I accept that traditional<br>
> stv (zero-order stv in relation to binomial stv) is a robust system,<br>
> in practise, as the Hare system of at-large stv/pr.<br>
<br>
As a ranked method, it must fail IIA, which means that strategy must<br>
sometimes be possible. And as it fails Condorcet, the obvious starting<br>
place to look is for an election where it doesn't pass Condorcet. For<br>
instance, this:<br>
<br>
549: A>B>C<br>
366: B>A>C<br>
366: B>C>A<br>
366: C>A>B<br>
<br>
A is the Condorcet winner. The first preferences are:<br>
A: 549, B: 732, C: 366<br>
and last preferences:<br>
A: 366, B: 366, C: 915<br>
<br>
so the ratios are:<br>
A: 366/549 = 0.67<br>
B: 366/732 = 0.5<br>
C: 915/366 = 2.5<br>
<br>
so B wins. Then the C>A>B voters have an incentive to vote A>C>B instead<br>
(compromising), after which the counts are:<br>
<br>
A: 366/915 = 0.29<br>
B: 366/732 = 0.5<br>
C: 915/0 = infinity<br>
<br>
and A wins. The C>A>B voters prefer A to B, so the strategy is to their<br>
benefit.<br>
<br>
It can be shown that, for methods where a majority can always force an<br>
outcome by coordinating how they vote, then modifying the method so that<br>
it elects the Condorcet winner if there is one never increases the<br>
proportion of elections where strategy is useful, and may indeed reduce it.<br>
<br>
> BSTV counts require values for all preference positions, which are<br>
> equal to the number of candidates. Any preference position may be an<br>
> abstention. A citizen who never voted but made an exception of their<br>
> dislike for Donald or Hilary could abstain on their first preference<br>
> but vote for either on their second preference, effecting an<br>
> exclusion, because there is only one vacancy.<br>
<br>
> That is the theory of it. I don't know how well it would work in<br>
> practise, because there never has been a practise. But I do know that<br>
> democracy is minimised, and evidently works badly, based on single<br>
> vacancies, in the Anglo-American systems.<br>
<br>
> Fully fledged binomial stv, FAB STV, does not work on less than 4 or <br>
> 5 member constituencies, the minimum requirement for a democracy of<br>
> all the people being represented by their choices.<br>
<br>
> Thank you for your examples. They have helped clarify my thinking -- somewhat!<br>
> According to my (accident-prone) working, A wins on a keep value of 38957/58966.<br>
> B also has a less than unity keep value of 38957/39366. The <br>
> difference is that one can say A has been elected on a quota of<br>
> 48961.5, with 58966 first preferences.<br>
> But B has not reached the elective quota. Tho B has not reached the<br>
> exclusion quota, that only says B has not been excluded.<br>
<br>
So by the keep values: A's first preference count is 58966 and last<br>
preference count is 38957, since the keep value is 38957/58966.<br>
<br>
You say that B's keep value is 38957/39366, i.e. first preference count<br>
of 39366 and last preference count of 38957. But that seems to be in<br>
reverse order. Indeed, your HTML page shows that it is 39366/38957.<br>
<br>
>From the keep values, it seems that truncations are not included when<br>
counting last preferences. I was pretty sure that BSTV would fail<br>
later-no-harm because the standard way of counting truncations, as STV<br>
does, is to consider everybody not ranked to be equal-ranked for last;<br>
and if you had done that, then it would be possible to induce later-no-harm.<br>
<br>
The good news is that you avoid this particular problem if you count<br>
anything past truncation simply as abstentions. So I guessed wrong,<br>
which was then cleared up by the example, which shows how useful they<br>
are :-)<br>
<br>
However, instead it seems that you get later-no-*help* failure. Consider<br>
this modified election:<br>
<br>
18125: A<br>
20035: A>B>C<br>
18722: A>C>B<br>
34488: B>A>C<br>
38634: C>B>A<br>
<br>
By my count, the first preferences are: A: 56882, B: 34488, C: 38634<br>
and the last preferences are: A: 38634, B: 18722, C: 54523<br>
and the last to first ratios are: A: 0.68, B: 0.54, C: 1.41<br>
<br>
so B wins. But if now the A voters fill out their ballot by voting<br>
A>C>B, then B's last preference count changes to 36847 and A wins<br>
instead. This is a violation of later-no-help.<br>
<br>
Ordinary STV passes both.<br>
<br>
I should note that Condorcet methods, that I prefer, fail both. My point<br>
isn't as much that later-no-harm and later-no-help are intrinsically<br>
good, as that it's much easier to check a claim by concrete evidence<br>
than by references to personal terminology (which may be hard to<br>
understand for others or take a lot of time to get acquainted with).<br>
<br>
<br>
On a final note, I would say that always counting truncation as<br>
abstention could lead to an unknown candidate problem: suppose there's a<br>
candidate who nobody has heard of and thus nobody bothers to rank. But<br>
he has a dedicated following all of whom rank him first. If nobody<br>
obtains a majority, then this candidate could win, e.g. something like:<br>
<br>
3300: A>B>C<br>
3300: B>C>A<br>
3200: C>A>B<br>
2: D<br>
<br>
I'm also not entirely sure what's going on with the quota transfers. If,<br>
in the single-winner case, someone who exceeds the quota is<br>
automatically elected, then there's no need for any transfers. However,<br>
if passing the quota doesn't guarantee victory, then later-no-harm<br>
failure might actually be possible. Suppose A is just above the quota<br>
and B is just below it (with B closer to the majority line), then if the<br>
A voters only vote for A, A might win; but if they vote A>B, then the<br>
surplus might be transferred to B and make B win. Perhaps. As I said,<br>
I'm not sure how the logic works in that case.<br>
<br>
-km<br>
----<br>
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</blockquote></div></div></div>