<div dir="auto"><br></div><div dir="auto">Colin—</div><div dir="auto"><br></div><div dir="auto">The incomprehension is indeed reciprocal. In this message I’ll try to reduce it, if not resolve it. <br></div><div dir="auto"><br></div><div dir="auto">These matters have been very much & very thoroughly discussed here, a long time ago. It might be best to either accept the consensus here, or to unassertively ask questions, to find out what the terms mean & why we say what we say.</div><div dir="auto"><br></div><div dir="auto">Don’t invent theory & tell us how it is.</div><div dir="auto"><br></div><div dir="auto">You have basically the right idea of what truncation & burying are.</div><div dir="auto"><br></div><div dir="auto">What you call “the rightful winner” is the social-utility maximizer. The Condorcet methods are intended to elect the Condorcet winner.</div><div dir="auto"><br></div><div dir="auto">You mention a 3rd winner you call the “sincere winner”. …presumably different from the Condorcet winner & the rightful winner. You didn’t say what you mean by that term.</div><div dir="auto"><br></div><div dir="auto">You’ve again spoken of “constant truncation”. How is that different from ordinary truncation? One habitually does it in every election? </div><div dir="auto"><br></div><div dir="auto">Did I say that the burier is trying to elect someone outside his own approval set?</div><div dir="auto"><br></div><div dir="auto">…or that the buriers’ candidate is the CW?</div><div dir="auto"><br></div><div dir="auto">Please try to be sure what you’re replying to, & what you mean, before posting.</div><div dir="auto"><br></div><div dir="auto">That “exonerated” post was about properties of the winning-votes methods. …properties that we discussed & agreed about long ago.</div><div dir="auto"><br></div><div dir="auto">Offensive truncation won’t work </div><div dir="auto"><br></div><div dir="auto">Offensive burial backfires if the CW’s voters haven’t ranked the buriers’ candidate.</div><div dir="auto"><br></div><div dir="auto">So, if you (a preferrer of the CW) refuse to rank anyone not in your approval set, then burial intended to change the winner from the CW to someone outside your approval set will backfire, & is thereby deterred.</div><div dir="auto"><br></div><div dir="auto">Michael Ossipoff </div><div dir="auto"><br><div class="gmail_quote" dir="auto"><div dir="ltr" class="gmail_attr">On Tue, Oct 3, 2023 at 00:11 Colin Champion <<a href="mailto:colin.champion@routemaster.app">colin.champion@routemaster.app</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">
<div>
<font face="Helvetica, Arial, sans-serif" style="font-family:Helvetica,Arial,sans-serif;color:rgb(0,0,0)">Michael - the
incomprehension is reciprocal. By burial I mean that the
supporters of one candidate A insincerely relegate another
candidate B to the bottom of their ballots. This is considered to
be successful if it leads to a candidate C winning who is closer
to A than the sincere winner is (where C may or may not be equal
to A). I assume that strategic voting will be attempted only when
it will succeed since I make no attempt to model imperfect
knowledge. <br>
The rightful winner is the candidate whose average distance
from voters is least. A voting method is deemed correct in an
election if it elects the rightful winner in spite of any attempt
at burial (i.e. against every (A,B) combination).<br>
With constant truncation, the relegated candidate is simply
truncated off. So, truncating from 8 to 4, if A's supporters agree
to bury B, and if B occurs in the top 4 positions of a voter's
ranking, then B is moved to the voter's discards and the ballot is
reduced to 3 candidates. If B is outside the top 4 positions, then
the burial has no effect. <br>
The likeliest case of successful burial is the opposite of the
case you say cannot happen. It arises when B is simultaneously the
Condorcet winner, the sincere winner and the rightful winner, and
when A obtains victory as a result of his supporters burying B. In
this case the buriers are *not* trying to change the winner to
someone outside their approval set and their candidate is *not*
the CW. I wonder whether your wording corresponds to your
intentions, or whether I simply misunderstand it. <br>
I'm afraid I also don't really understand your 'exonerated'
post, but it probably isn't directed at me. <br></font></div><div><font face="Helvetica, Arial, sans-serif" style="font-family:Helvetica,Arial,sans-serif;color:rgb(0,0,0)">
Colin<br>
</font><br>
<div>On 02/10/2023 19:32, Michael Ossipoff
wrote:<br>
</div>
<blockquote type="cite">
<div><br>
</div>
<div><br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">---------- Forwarded message
---------<br>
From: <strong class="gmail_sendername" dir="auto">Michael
Ossipoff</strong> <span dir="auto"><<a href="mailto:email9648742@gmail.com" target="_blank">email9648742@gmail.com</a>></span><br>
Date: Mon, Oct 2, 2023 at 11:32<br>
Subject: Re: [EM] Fwd: Ranked Pairs<br>
To: Colin Champion <<a href="mailto:colin.champion@routemaster.app" target="_blank">colin.champion@routemaster.app</a>><br>
</div>
<br>
<br>
<div dir="auto">You aren’t being very clear with us regarding
the sense in which you mean that margins beats wv at
“constant” burial.</div>
<div dir="auto"><br>
</div>
<div dir="auto">With wv, if your candidate is CW, & you
refuse to rank candidates outside your approval-set, then an
attempt to use burial to change the winner to someone
outside your approval-set will backfire.</div>
<div><br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Mon, Oct 2, 2023 at
06:48 Colin Champion <<a href="mailto:colin.champion@routemaster.app" target="_blank">colin.champion@routemaster.app</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">
<div> <font face="Helvetica, Arial, sans-serif" style="font-family:Helvetica,Arial,sans-serif;color:rgb(0,0,0)">And
here, as promised, are some results for strategic
voting. <br>
<br>
* Constant truncation: WV beats margins for sincere
voting, and also for compromising and false cycles,
but margins beats WV by quite a long way (2.7%) for
burial.<br>
* Approval truncation: margins beats WV for sincere
voting. The two methods almost tie under
compromising; margins wins by a long way under false
cycles (5.5%) and under burial.<br>
* Candidate-specific truncation: WV beats margins
for sincere voting; it also wins (slightly more
convincingly) under compromising; it loses under
false cycles and burial.<br>
* Ignorance truncation: this was essentially a tie
under sincere voting and remains one under
compromising; margins wins slightly under false
cycles and burial.<br>
<br>
Approval truncation takes place before a voter's
strategic reordering of candidates; other forms of
truncation take place after it. In each case I
measure the accuracy of a voting method in the
presence of strategic voting, not the vulnerability
of the method to manipulation.<br>
CJC<br>
</font></div>
<div><br>
<div>On 28/09/2023 13:00, Colin Champion wrote:<br>
</div>
<blockquote type="cite"> <font face="Helvetica,
Arial, sans-serif" style="font-family:Helvetica,Arial,sans-serif;color:rgb(0,0,0)">I tried two other forms of
truncation. Under "candidate-specific truncation"
the m candidates have associated truncation levels
which are a random permutation of the numbers
1...m. A ballot is truncated to the level
corresponding to its first candidate. I expected
this to be a hard case for WV, but in fact it does
appreciably better than margins. </font><br>
<font face="monospace" style="font-family:monospace;color:rgb(0,0,0)"> random
fptp dblv seq conting nauru
borda sbc2 bucklin sinkhorn mj
av coombs <br>
12.6630 35.6490 50.7000 44.9140
51.6650 54.5890 73.6530 - 66.3850
- - 53.3880 68.9630 <br>
clower knockout spe benham
btr-irv baldwin nanson minimax minimaxwv
minisum rp river schulze asm
cupper <br>
70.0190 71.5400 71.7760 71.2680
70.9510 71.4700 71.8440 72.0970 72.9090
72.1000 71.5630 71.9420 71.3330 72.2980
75.2630 <br>
condorcet+ random fptp dblv conting
borda av <br>
70.6780 70.6580 70.9080 71.0760
72.2750 70.9920 <br>
llull+ randomr fptpf fptpr dblvf
contingr bordaf bordar avf avr
minimaxf minimaxr<br>
71.6220 71.2570 71.9820 71.2600
71.9970 72.2020 72.0080 71.3300 72.0120
72.0510 72.0070 <br>
smith+ randomr fptpf fptpr dblvf
contingr bordaf bordar avf avr
minimaxf minimaxr tideman <br>
71.3330 70.8970 71.5080 70.9620
71.5820 72.2730 71.6550 71.0270 71.6240
72.0990 71.6490 71.1760 <br>
</font><br>
The other form I tried was 'ignorance truncation'.
Each candidate has a prominence - i.e. probability
of being recognised by an arbitrary voter - drawn
(separately for each election) from a Beta(r,s)
distribution. Voters rank the candidates they
recognise in order of proximity, truncating after
the last candidate they recognise. I used r=2, s=1,
giving a recognition probability of 2/3. This was
essentially a tie between the two minimax variants.
Borda, which looked good against other forms of
truncation, did badly this time. Evidently ignorance
truncation is more damaging than the other sorts. <br>
<font face="monospace" style="font-family:monospace;color:rgb(0,0,0)"> random
fptp dblv seq conting nauru
borda sbc2 bucklin sinkhorn mj
av coombs <br>
12.5510 37.4290 43.1720 36.6340
41.2690 40.7330 34.6170 - 41.5260
- - 40.9330 42.4740 <br>
clower knockout spe benham
btr-irv baldwin nanson minimax minimaxwv
minisum rp river schulze asm
cupper <br>
43.1770 43.8040 44.4050 43.5870
44.0050 44.0480 43.9970 43.9990 43.9330
44.0170 43.8610 44.0040 43.7660 43.6000
46.7470 <br>
condorcet+ random fptp dblv conting
borda av <br>
43.6260 44.0730 44.1880 43.9420
43.2570 43.5720 <br>
llull+ randomr fptpf fptpr dblvf
contingr bordaf bordar avf avr
minimaxf minimaxr<br>
43.7980 43.9980 43.4990 44.0330
43.4980 43.3220 43.4960 43.6550 43.4950
43.9890 43.4980 <br>
smith+ randomr fptpf fptpr dblvf
contingr bordaf bordar avf avr
minimaxf minimaxr tideman <br>
43.7660 44.1030 43.4060 44.1810
43.4080 43.2570 43.4000 43.5750 43.4000
44.0000 43.4100 43.5840 </font><br>
At risk of repetition... correctness of software is
not guaranteed.<br>
CJC<br>
<br>
<div>On 27/09/2023 12:45, Colin Champion wrote:<br>
</div>
<blockquote type="cite"> <font face="Helvetica,
Arial, sans-serif" style="font-family:Helvetica,Arial,sans-serif;color:rgb(0,0,0)">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" style="font-family:monospace;color:rgb(0,0,0)"><font face="Helvetica,
Arial, sans-serif" style="font-family:Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><font face="monospace" style="font-family:monospace;color:rgb(0,0,0)">
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>On 24/09/2023 13:41, Colin Champion wrote:<br>
</div>
<blockquote type="cite"> <font face="Helvetica,
Arial, sans-serif" style="font-family:Helvetica,Arial,sans-serif;color:rgb(0,0,0)">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>On 23/09/2023 02:47, Kevin Venzke wrote:<br>
</div>
<blockquote type="cite">
<pre style="font-family:monospace">Hi Colin,
Le vendredi 22 septembre 2023 à 02:57:42 UTC−5, Colin Champion <a href="mailto:colin.champion@routemaster.app" target="_blank" style="font-family:monospace"><colin.champion@routemaster.app></a> a écrit :
</pre>
<blockquote type="cite">
<pre style="font-family:monospace">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 style="font-family:monospace">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 <a href="http://votingmethods.net/calc" target="_blank" style="font-family:monospace">votingmethods.net/calc</a> 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
<a href="http://votingmethods.net" target="_blank" style="font-family:monospace">votingmethods.net</a>
</pre>
</blockquote>
<br>
<br>
<fieldset></fieldset>
<pre style="font-family:monospace">----
Election-Methods mailing list - see <a href="https://electorama.com/em" target="_blank" style="font-family:monospace">https://electorama.com/em</a> for list info
</pre>
</blockquote>
<br>
</blockquote>
<br>
<br>
<fieldset></fieldset>
<pre style="font-family:monospace">----
Election-Methods mailing list - see <a href="https://electorama.com/em" target="_blank" style="font-family:monospace">https://electorama.com/em</a> for list info
</pre>
</blockquote>
<br>
</div>
----<br>
Election-Methods mailing list - see <a href="https://electorama.com/em" rel="noreferrer" target="_blank">https://electorama.com/em</a>
for list info<br>
</blockquote>
</div>
</div>
</div>
</div>
<br>
<fieldset></fieldset>
<pre style="font-family:monospace">----
Election-Methods mailing list - see <a href="https://electorama.com/em" target="_blank" style="font-family:monospace">https://electorama.com/em</a> for list info
</pre>
</blockquote>
<br>
</div>
----<br>
Election-Methods mailing list - see <a href="https://electorama.com/em" rel="noreferrer" target="_blank">https://electorama.com/em</a> for list info<br>
</blockquote></div></div>