<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
</head>
<body>
<font face="Helvetica, Arial, sans-serif">I have some preliminary
results for "approval truncation" in which a voter truncates at
the largest gap between cardinal rankings. Minimax (margins) does
slightly better than minimax (WV). Voting is sincere; there are 8
candidates and 10001 voters (a ballot is truncated on average to
4.6 entries). Full figures follow (which won't be very readable in
a variable-width font). It's noticeable that the results are worse
than for fixed truncation, even though the average ballot length
is slightly greater. <br>
<font face="monospace"><font face="Helvetica, Arial, sans-serif"><font
face="monospace"> random fptp dblv
seq conting nauru borda sbc2 bucklin
sinkhorn mj av coombs <br>
12.5820 35.9910 - 45.8790 -
53.6880 80.5090 - 67.5170 - -
55.7040 69.1810 <br>
clower knockout spe benham btr-irv
baldwin nanson minimax minimaxwv minisum rp
river schulze asm cupper <br>
75.1840 75.8440 76.2830 76.0300 75.8900
75.8700 75.9440 75.9660 75.9580 75.9680 75.8200
- 75.7640 75.9200 77.3430 <br>
condorcet+ random fptp dblv conting borda
av <br>
75.4610 75.5690 75.6860 75.8110 76.4530
75.8300 <br>
llull+ randomr fptpf fptpr dblvf contingr
bordaf bordar avf avr minimaxf minimaxr<br>
75.8750 75.8660 76.2610 75.8330 76.2600
76.3780 76.2620 75.9250 76.2590 75.9530 76.2620 <br>
smith+ randomr fptpf fptpr dblvf contingr
bordaf bordar avf avr minimaxf minimaxr tideman
<br>
75.7640 75.7470 76.2310 75.7630 76.2400
76.4530 76.2530 75.8650 76.2420 75.9680 76.2470
76.0700 </font><br>
</font></font>I will try a couple of other truncation models and
then look at strategic voting.<br>
CJC<br>
</font><br>
<div class="moz-cite-prefix">On 24/09/2023 13:41, Colin Champion
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:33c95bb4-0b5b-7b8e-3180-6b0a817c0809@routemaster.app">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<font face="Helvetica, Arial, sans-serif">Kevin – thanks for this
helpful reply. I'm inclined to favour viewing a tie as two
half-voters with opposed preferences. I admit that this can only
be a rule of thumb, but I find it quite persuasive. After all,
the whole point of ranked voting is that voters start out, I
assume, with nebulous cardinal judgements in their heads, and
that turning these judgements into rankings puts them onto a
common basis (albeit with loss of information) which allows them
to be meaningfully combined. The WV rule could easily undermine
the premise of this procedure. <br>
I believe that asymmetric treatment of ties in the Borda
count leads quite directly to errors of the sort I described,
but I don't know if this is widely accepted. <br>
It's true that Darlington models ties as genuine expressions
of indifference. In practice ties can mean almost anything;
indifference, laziness, ignorance... Quite possibly voting
methods which work well for one sort of tie will work less well
for another. The result I produced myself is probably genuine,
and indicates that WV is more accurate than margins for
mandatory truncation; but I was wrong to suppose that it could
be interpreted more generally since it omits the effect which is
most likely to work against WV.<br>
As for the positive arguments you put forward, well they
might justify a rule of thumb but I wouldn't find them
compelling. I don't find the Condorcet principle persuasive on
its own merits (and do not believe it generally sound), but I
accept it as a working principle because I don't know any other
way of obtaining simple accurate voting methods under a spatial
model. <br>
I will try to extend my own evaluation software to allow a
less restrictive model of truncation.<br>
Colin<br>
</font><br>
<div class="moz-cite-prefix">On 23/09/2023 02:47, Kevin Venzke
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:2129168188.8275917.1695433672418@mail.yahoo.com">
<pre class="moz-quote-pre" wrap="">Hi Colin,
Le vendredi 22 septembre 2023 à 02:57:42 UTC−5, Colin Champion <a class="moz-txt-link-rfc2396E" href="mailto:colin.champion@routemaster.app" moz-do-not-send="true"><colin.champion@routemaster.app></a> a écrit :
</pre>
<blockquote type="cite">
<pre class="moz-quote-pre" wrap="">A possible explanation for the discrepancy between my result and Darlington's is that
in my evaluation every ballot had the same number of ties and in Darlington's the
numbers differed.
On the face of it, WV doesn't treat voters equally. If we defined "winning votes" as
"the number of voters who prefer A to B plus half the number who rank them equally",
then every voter would contribute m(m-1)/2 winning votes and WV would be equivalent
(I think) to Margins. But instead we define winning votes asymmetrically so that WV
is *not* equivalent to margins but voters contribute different numbers of winning
votes depending on the number of ties in their ballots. I can imagine this leading to
artefacts which Darlington's evaluation would pick up and mine would miss. If this is
what happened, then even Darlington's evaluation must be too lenient to WV since he
doesn't include effects which would in fact arise, such as voters truncating
differentially according to their political viewpoint.
Maybe these things have been taken into account; I have no idea, having never seen the
thinking behind WV.
</pre>
</blockquote>
<pre class="moz-quote-pre" wrap="">I am not sure what to make of Darlington's defeat strength comparison. It sounds like
it was basically a simulation of sincere voters who vote equality because they actually
consider the candidates equal. That premise is fine but somewhat far removed from how
this topic is usually discussed, i.e. with some consideration of comparative strategy.
I notice incidentally that Darlington says incorrectly on page 22 that MinMax(PO) is a
Condorcet method. I wonder whether he implemented it as one to get his numbers on that.
In any case:
To find the motivation for WV I would start with first principles. How should we design
a Condorcet completion method to minimize strategic incentives? A motivation behind
Condorcet itself is that voters should not vote sincerely only to find that they
should've voted another way.
What could this mean here? Well, a full majority can always get what they want by
changing their votes. Therefore if a majority votes A>B yet B is elected, we have
*probably* done something wrong, because the majority certainly did have the power to
make A win instead. The election of B gives the A>B voters an incentive to vote
differently to change the outcome. The voters obtain a "complaint," I will call it.
Since majorities will most predictably obtain such complaints when we override their
preference, we should prioritize locking majorities.
With WV, there is no special heed paid to majorities, it just goes down the list of
contests starting with the largest winning blocs. But this achieves the goal. It
applies its principle to sub-majority contests as well, and maybe this is good bad or
neutral, but maybe we can believe that if it was helpful (for our end goal) to favor
majorities over sub-majorities then it could also be helpful to favor larger
sub-majorities over smaller sub-majorities. It certainly stands to reason that the more
voters you have sharing some stance, the more likely it is that a vote change on their
part could change the outcome.
(On my website I describe a different approach focused on compromise incentive, and
measuring the potential for this more directly, and one can take that as me suggesting
that WV actually leaves some room for improvement.)
You notice that adding half-votes to equal rankings under WV will turn it into margins.
This would give every contest a full majority on the winning side, and seemingly we can
trivialize this requirement of mine to prioritize majorities.
But I think it's clear, in the context of this analysis, that adding half-votes for
equal rankings doesn't make sense. The voter who says A=B doesn't turn into a pair of
opposing "half-complaints," where one of the complaints has the potential to be voiced
when *either* of A or B is elected. The A=B voter has no possible complaint either way,
as neither result can incentivize them to change their vote.
Additionally, I think that voters expect and want it to be the case that abstaining
from a pairwise contest does not mean the same thing as saying they rate both
candidates equal. I touched on this in my previous post.
Consider this election:
7 A>B
5 B
8 C
Margins elects A, which is very unusual across election methods, and I think most
people would find this result surprising due to a sense of what truncation ought to
mean.
(Consider copying it into votingmethods.net/calc to see margins and MMPO stand alone
here.)
Perhaps with enough education people can *understand* that the method takes seriously
the apparent equality of the truncated preferences. But I don't think voters will find
it comfortable to vote under those circumstances. I think voters want to be able to
identify the set of candidates that they believe they are trying to defeat, leave them
out of their ranking, and not have to think any further about it.
Kevin
votingmethods.net
</pre>
</blockquote>
<br>
<br>
<fieldset class="mimeAttachmentHeader"></fieldset>
<pre class="moz-quote-pre" wrap="">----
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>
<br>
</body>
</html>