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<font face="Helvetica, Arial, sans-serif">Michael – apologies. By
the 'sincere winner' I mean the candidate who would win in the
absence of strategic voting. By 'constant truncation' I mean all
voters truncating to the same number of candidates. This models
the mandatory truncation which is imposed in some elections, in
which a voter is limited to ranking (eg.) 3 candidates. It differs
from truncation to differing numbers of candidates such as would
arise from voter indifference or incomplete knowledge. <br>
If Condorcet methods are intended to elect the Condorcet
winner, then I suppose they're 100% successful. For that matter
the Borda count is 100% successful at electing the Borda winner. <br>
You wrote "</font><font face="Helvetica, Arial, sans-serif">if
your candidate is CW... then an attempt to use burial to change
the winner to someone outside your approval-set will backfire"
which I understood as implying that "you" were the burier. Perhaps
you meant that if Ursula, a supporter of B, refuses to rank anyone
outside her "approval set", then if another voter Veronica tries
to change the winner from B to A (who is not in Ursula's approval
set) then the attempt would backfire. <br>
Colin<br>
</font><br>
<div class="moz-cite-prefix">On 03/10/2023 09:13, Michael Ossipoff
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAOKDY5AzoRtZ4x98HG-tJjrkTLjJNQbFjNwU0u6ovs=2JQ1FWg@mail.gmail.com">
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<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"
moz-do-not-send="true">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
style="font-family:Helvetica,Arial,sans-serif;color:rgb(0,0,0)"
face="Helvetica, Arial, sans-serif">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
style="font-family:Helvetica,Arial,sans-serif;color:rgb(0,0,0)"
face="Helvetica, Arial, sans-serif"> 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" moz-do-not-send="true">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" moz-do-not-send="true">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" moz-do-not-send="true">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
style="font-family:Helvetica,Arial,sans-serif;color:rgb(0,0,0)"
face="Helvetica, Arial, sans-serif">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
style="font-family:Helvetica,Arial,sans-serif;color:rgb(0,0,0)"
face="Helvetica, Arial, sans-serif">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
style="font-family:monospace;color:rgb(0,0,0)"
face="monospace"> 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
style="font-family:monospace;color:rgb(0,0,0)"
face="monospace"> 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
style="font-family:Helvetica,Arial,sans-serif;color:rgb(0,0,0)"
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
style="font-family:monospace;color:rgb(0,0,0)"
face="monospace"><font
style="font-family:Helvetica,Arial,sans-serif;color:rgb(0,0,0)"
face="Helvetica, Arial,
sans-serif"><font
style="font-family:monospace;color:rgb(0,0,0)"
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>On 24/09/2023 13:41, Colin Champion
wrote:<br>
</div>
<blockquote type="cite"> <font
style="font-family:Helvetica,Arial,sans-serif;color:rgb(0,0,0)"
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>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" moz-do-not-send="true"><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" moz-do-not-send="true">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" moz-do-not-send="true">votingmethods.net</a>
</pre>
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