Fwd: Fwd: Ranked Pairs
---------- Forwarded message ---------
From: Michael Ossipoff email9648742@gmail.com
Date: Mon, Oct 2, 2023 at 11:32
Subject: Re: [EM] Fwd: Ranked Pairs
To: Colin Champion colin.champion@routemaster.app
You aren’t being very clear with us regarding the sense in which you mean
that margins beats wv at “constant” burial.
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.
On Mon, Oct 2, 2023 at 06:48 Colin Champion colin.champion@routemaster.app
wrote:
And here, as promised, are some results for strategic voting.
- 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. - 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. - Candidate-specific truncation: WV beats margins for sincere voting; it
also wins (slightly more convincingly) under compromising; it loses under
false cycles and burial. - Ignorance truncation: this was essentially a tie under sincere voting
and remains one under compromising; margins wins slightly under false
cycles and burial.
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.
CJC
On 28/09/2023 13:00, Colin Champion wrote:
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.
random fptp dblv seq conting nauru
borda sbc2 bucklin sinkhorn mj av coombs
12.6630 35.6490 50.7000 44.9140 51.6650 54.5890
73.6530 - 66.3850 - - 53.3880 68.9630
clower knockout spe benham btr-irv baldwin nanson
minimax minimaxwv minisum rp river schulze asm cupper
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
condorcet+ random fptp dblv conting borda av
70.6780 70.6580 70.9080 71.0760 72.2750 70.9920
llull+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr
71.6220 71.2570 71.9820 71.2600 71.9970 72.2020 72.0080
71.3300 72.0120 72.0510 72.0070
smith+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr tideman
71.3330 70.8970 71.5080 70.9620 71.5820 72.2730 71.6550
71.0270 71.6240 72.0990 71.6490 71.1760
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.
random fptp dblv seq conting nauru
borda sbc2 bucklin sinkhorn mj av coombs
12.5510 37.4290 43.1720 36.6340 41.2690 40.7330
34.6170 - 41.5260 - - 40.9330 42.4740
clower knockout spe benham btr-irv baldwin nanson
minimax minimaxwv minisum rp river schulze asm cupper
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
condorcet+ random fptp dblv conting borda av
43.6260 44.0730 44.1880 43.9420 43.2570 43.5720
llull+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr
43.7980 43.9980 43.4990 44.0330 43.4980 43.3220 43.4960
43.6550 43.4950 43.9890 43.4980
smith+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr tideman
43.7660 44.1030 43.4060 44.1810 43.4080 43.2570 43.4000
43.5750 43.4000 44.0000 43.4100 43.5840
At risk of repetition... correctness of software is not guaranteed.
CJC
On 27/09/2023 12:45, Colin Champion wrote:
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.
random fptp dblv seq conting nauru
borda sbc2 bucklin sinkhorn mj av coombs
12.5820 35.9910 - 45.8790 - 53.6880
80.5090 - 67.5170 - - 55.7040 69.1810
clower knockout spe benham btr-irv baldwin nanson
minimax minimaxwv minisum rp river schulze asm cupper
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
condorcet+ random fptp dblv conting borda av
75.4610 75.5690 75.6860 75.8110 76.4530 75.8300
llull+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr
75.8750 75.8660 76.2610 75.8330 76.2600 76.3780 76.2620
75.9250 76.2590 75.9530 76.2620
smith+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr tideman
75.7640 75.7470 76.2310 75.7630 76.2400 76.4530 76.2530
75.8650 76.2420 75.9680 76.2470 76.0700
I will try a couple of other truncation models and then look at strategic
voting.
CJC
On 24/09/2023 13:41, Colin Champion wrote:
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.
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.
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.
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.
I will try to extend my own evaluation software to allow a less
restrictive model of truncation.
Colin
On 23/09/2023 02:47, Kevin Venzke wrote:
Hi Colin,
Le vendredi 22 septembre 2023 à 02:57:42 UTC−5, Colin Champion colin.champion@routemaster.app colin.champion@routemaster.app a écrit :
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.
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.
Kevinvotingmethods.net
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list
info
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.
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).
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.
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.
I'm afraid I also don't really understand your 'exonerated' post,
but it probably isn't directed at me.
Colin
On 02/10/2023 19:32, Michael Ossipoff wrote:
---------- Forwarded message ---------
From: Michael Ossipoff <email9648742@gmail.com
mailto:email9648742@gmail.com>
Date: Mon, Oct 2, 2023 at 11:32
Subject: Re: [EM] Fwd: Ranked Pairs
To: Colin Champion <colin.champion@routemaster.app
mailto:colin.champion@routemaster.app>
You aren’t being very clear with us regarding the sense in which you
mean that margins beats wv at “constant” burial.
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.
On Mon, Oct 2, 2023 at 06:48 Colin Champion
<colin.champion@routemaster.app
mailto:colin.champion@routemaster.app> wrote:
And here, as promised, are some results for strategic voting.
* 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.
* 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.
* Candidate-specific truncation: WV beats margins for sincere
voting; it also wins (slightly more convincingly) under
compromising; it loses under false cycles and burial.
* Ignorance truncation: this was essentially a tie under sincere
voting and remains one under compromising; margins wins slightly
under false cycles and burial.
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.
CJC
On 28/09/2023 13:00, Colin Champion wrote:
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.
random fptp dblv seq conting nauru
borda sbc2 bucklin sinkhorn mj av coombs
12.6630 35.6490 50.7000 44.9140 51.6650 54.5890
73.6530 - 66.3850 - - 53.3880 68.9630
clower knockout spe benham btr-irv baldwin
nanson minimax minimaxwv minisum rp river schulze
asm cupper
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
condorcet+ random fptp dblv conting borda av
70.6780 70.6580 70.9080 71.0760 72.2750 70.9920
llull+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr
71.6220 71.2570 71.9820 71.2600 71.9970 72.2020
72.0080 71.3300 72.0120 72.0510 72.0070
smith+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr tideman
71.3330 70.8970 71.5080 70.9620 71.5820 72.2730
71.6550 71.0270 71.6240 72.0990 71.6490 71.1760
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.
random fptp dblv seq conting nauru
borda sbc2 bucklin sinkhorn mj av coombs
12.5510 37.4290 43.1720 36.6340 41.2690 40.7330
34.6170 - 41.5260 - - 40.9330 42.4740
clower knockout spe benham btr-irv baldwin
nanson minimax minimaxwv minisum rp river schulze
asm cupper
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
condorcet+ random fptp dblv conting borda av
43.6260 44.0730 44.1880 43.9420 43.2570 43.5720
llull+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr
43.7980 43.9980 43.4990 44.0330 43.4980 43.3220
43.4960 43.6550 43.4950 43.9890 43.4980
smith+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr tideman
43.7660 44.1030 43.4060 44.1810 43.4080 43.2570
43.4000 43.5750 43.4000 44.0000 43.4100 43.5840
At risk of repetition... correctness of software is not guaranteed.
CJC
On 27/09/2023 12:45, Colin Champion wrote:
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.
random fptp dblv seq conting nauru borda
sbc2 bucklin sinkhorn mj av coombs
12.5820 35.9910 - 45.8790 - 53.6880
80.5090 - 67.5170 - - 55.7040 69.1810
clower knockout spe benham btr-irv baldwin
nanson minimax minimaxwv minisum rp river schulze
asm cupper
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
condorcet+ random fptp dblv conting borda av
75.4610 75.5690 75.6860 75.8110 76.4530 75.8300
llull+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr
75.8750 75.8660 76.2610 75.8330 76.2600 76.3780
76.2620 75.9250 76.2590 75.9530 76.2620
smith+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr tideman
75.7640 75.7470 76.2310 75.7630 76.2400 76.4530
76.2530 75.8650 76.2420 75.9680 76.2470 76.0700
I will try a couple of other truncation models and then look at
strategic voting.
CJC
On 24/09/2023 13:41, Colin Champion wrote:
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.
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.
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.
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.
I will try to extend my own evaluation software to allow a
less restrictive model of truncation.
Colin
On 23/09/2023 02:47, Kevin Venzke wrote:
Hi Colin,
Le vendredi 22 septembre 2023 à 02:57:42 UTC−5, Colin Champion<colin.champion@routemaster.app> <mailto:colin.champion@routemaster.app> a écrit :
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.
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 intovotingmethods.net/calc <http://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 <http://votingmethods.net>
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Colin—
The incomprehension is indeed reciprocal. In this message I’ll try to
reduce it, if not resolve it.
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.
Don’t invent theory & tell us how it is.
You have basically the right idea of what truncation & burying are.
What you call “the rightful winner” is the social-utility maximizer. The
Condorcet methods are intended to elect the Condorcet winner.
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.
You’ve again spoken of “constant truncation”. How is that different from
ordinary truncation? One habitually does it in every election?
Did I say that the burier is trying to elect someone outside his own
approval set?
…or that the buriers’ candidate is the CW?
Please try to be sure what you’re replying to, & what you mean, before
posting.
That “exonerated” post was about properties of the winning-votes methods.
…properties that we discussed & agreed about long ago.
Offensive truncation won’t work
Offensive burial backfires if the CW’s voters haven’t ranked the buriers’
candidate.
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.
Michael Ossipoff
On Tue, Oct 3, 2023 at 00:11 Colin Champion colin.champion@routemaster.app
wrote:
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.
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).
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.
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.
I'm afraid I also don't really understand your 'exonerated' post, but
it probably isn't directed at me.
Colin
On 02/10/2023 19:32, Michael Ossipoff wrote:
---------- Forwarded message ---------
From: Michael Ossipoff email9648742@gmail.com
Date: Mon, Oct 2, 2023 at 11:32
Subject: Re: [EM] Fwd: Ranked Pairs
To: Colin Champion colin.champion@routemaster.app
You aren’t being very clear with us regarding the sense in which you mean
that margins beats wv at “constant” burial.
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.
On Mon, Oct 2, 2023 at 06:48 Colin Champion <
colin.champion@routemaster.app> wrote:
And here, as promised, are some results for strategic voting.
- 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. - 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. - Candidate-specific truncation: WV beats margins for sincere voting; it
also wins (slightly more convincingly) under compromising; it loses under
false cycles and burial. - Ignorance truncation: this was essentially a tie under sincere voting
and remains one under compromising; margins wins slightly under false
cycles and burial.
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.
CJC
On 28/09/2023 13:00, Colin Champion wrote:
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.
random fptp dblv seq conting nauru
borda sbc2 bucklin sinkhorn mj av coombs
12.6630 35.6490 50.7000 44.9140 51.6650 54.5890
73.6530 - 66.3850 - - 53.3880 68.9630
clower knockout spe benham btr-irv baldwin nanson
minimax minimaxwv minisum rp river schulze asm cupper
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
condorcet+ random fptp dblv conting borda av
70.6780 70.6580 70.9080 71.0760 72.2750 70.9920
llull+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr
71.6220 71.2570 71.9820 71.2600 71.9970 72.2020 72.0080
71.3300 72.0120 72.0510 72.0070
smith+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr tideman
71.3330 70.8970 71.5080 70.9620 71.5820 72.2730 71.6550
71.0270 71.6240 72.0990 71.6490 71.1760
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.
random fptp dblv seq conting nauru
borda sbc2 bucklin sinkhorn mj av coombs
12.5510 37.4290 43.1720 36.6340 41.2690 40.7330
34.6170 - 41.5260 - - 40.9330 42.4740
clower knockout spe benham btr-irv baldwin nanson
minimax minimaxwv minisum rp river schulze asm cupper
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
condorcet+ random fptp dblv conting borda av
43.6260 44.0730 44.1880 43.9420 43.2570 43.5720
llull+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr
43.7980 43.9980 43.4990 44.0330 43.4980 43.3220 43.4960
43.6550 43.4950 43.9890 43.4980
smith+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr tideman
43.7660 44.1030 43.4060 44.1810 43.4080 43.2570 43.4000
43.5750 43.4000 44.0000 43.4100 43.5840
At risk of repetition... correctness of software is not guaranteed.
CJC
On 27/09/2023 12:45, Colin Champion wrote:
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.
random fptp dblv seq conting nauru
borda sbc2 bucklin sinkhorn mj av coombs
12.5820 35.9910 - 45.8790 - 53.6880
80.5090 - 67.5170 - - 55.7040 69.1810
clower knockout spe benham btr-irv baldwin nanson
minimax minimaxwv minisum rp river schulze asm cupper
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
condorcet+ random fptp dblv conting borda av
75.4610 75.5690 75.6860 75.8110 76.4530 75.8300
llull+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr
75.8750 75.8660 76.2610 75.8330 76.2600 76.3780 76.2620
75.9250 76.2590 75.9530 76.2620
smith+ randomr fptpf fptpr dblvf contingr bordaf
bordar avf avr minimaxf minimaxr tideman
75.7640 75.7470 76.2310 75.7630 76.2400 76.4530 76.2530
75.8650 76.2420 75.9680 76.2470 76.0700
I will try a couple of other truncation models and then look at strategic
voting.
CJC
On 24/09/2023 13:41, Colin Champion wrote:
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.
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.
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.
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.
I will try to extend my own evaluation software to allow a less
restrictive model of truncation.
Colin
On 23/09/2023 02:47, Kevin Venzke wrote:
Hi Colin,
Le vendredi 22 septembre 2023 à 02:57:42 UTC−5, Colin Champion colin.champion@routemaster.app colin.champion@routemaster.app a écrit :
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.
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.
Kevinvotingmethods.net
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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.
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.
You wrote "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.
Colin
On 03/10/2023 09:13, Michael Ossipoff wrote:
Colin—
The incomprehension is indeed reciprocal. In this message I’ll try to
reduce it, if not resolve it.
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.
Don’t invent theory & tell us how it is.
You have basically the right idea of what truncation & burying are.
What you call “the rightful winner” is the social-utility maximizer.
The Condorcet methods are intended to elect the Condorcet winner.
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.
You’ve again spoken of “constant truncation”. How is that different
from ordinary truncation? One habitually does it in every election?
Did I say that the burier is trying to elect someone outside his own
approval set?
…or that the buriers’ candidate is the CW?
Please try to be sure what you’re replying to, & what you mean, before
posting.
That “exonerated” post was about properties of the winning-votes
methods. …properties that we discussed & agreed about long ago.
Offensive truncation won’t work
Offensive burial backfires if the CW’s voters haven’t ranked the
buriers’ candidate.
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.
Michael Ossipoff
On Tue, Oct 3, 2023 at 00:11 Colin Champion
<colin.champion@routemaster.app
mailto:colin.champion@routemaster.app> wrote:
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.
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).
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.
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.
I'm afraid I also don't really understand your 'exonerated'
post, but it probably isn't directed at me.
Colin
On 02/10/2023 19:32, Michael Ossipoff wrote:
---------- Forwarded message ---------
From: *Michael Ossipoff* <email9648742@gmail.com
<mailto:email9648742@gmail.com>>
Date: Mon, Oct 2, 2023 at 11:32
Subject: Re: [EM] Fwd: Ranked Pairs
To: Colin Champion <colin.champion@routemaster.app
<mailto:colin.champion@routemaster.app>>
You aren’t being very clear with us regarding the sense in which
you mean that margins beats wv at “constant” burial.
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.
On Mon, Oct 2, 2023 at 06:48 Colin Champion
<colin.champion@routemaster.app
<mailto:colin.champion@routemaster.app>> wrote:
And here, as promised, are some results for strategic voting.
* 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.
* 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.
* Candidate-specific truncation: WV beats margins for sincere
voting; it also wins (slightly more convincingly) under
compromising; it loses under false cycles and burial.
* Ignorance truncation: this was essentially a tie under
sincere voting and remains one under compromising; margins
wins slightly under false cycles and burial.
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.
CJC
On 28/09/2023 13:00, Colin Champion wrote:
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.
random fptp dblv seq conting nauru
borda sbc2 bucklin sinkhorn mj av coombs
12.6630 35.6490 50.7000 44.9140 51.6650
54.5890 73.6530 - 66.3850 - - 53.3880 68.9630
clower knockout spe benham btr-irv
baldwin nanson minimax minimaxwv minisum rp river
schulze asm cupper
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
condorcet+ random fptp dblv conting borda av
70.6780 70.6580 70.9080 71.0760 72.2750 70.9920
llull+ randomr fptpf fptpr dblvf contingr
bordaf bordar avf avr minimaxf minimaxr
71.6220 71.2570 71.9820 71.2600 71.9970
72.2020 72.0080 71.3300 72.0120 72.0510 72.0070
smith+ randomr fptpf fptpr dblvf contingr
bordaf bordar avf avr minimaxf minimaxr tideman
71.3330 70.8970 71.5080 70.9620 71.5820
72.2730 71.6550 71.0270 71.6240 72.0990 71.6490 71.1760
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.
random fptp dblv seq conting nauru
borda sbc2 bucklin sinkhorn mj av coombs
12.5510 37.4290 43.1720 36.6340 41.2690
40.7330 34.6170 - 41.5260 - - 40.9330 42.4740
clower knockout spe benham btr-irv
baldwin nanson minimax minimaxwv minisum rp river
schulze asm cupper
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
condorcet+ random fptp dblv conting borda av
43.6260 44.0730 44.1880 43.9420 43.2570 43.5720
llull+ randomr fptpf fptpr dblvf contingr
bordaf bordar avf avr minimaxf minimaxr
43.7980 43.9980 43.4990 44.0330 43.4980
43.3220 43.4960 43.6550 43.4950 43.9890 43.4980
smith+ randomr fptpf fptpr dblvf contingr
bordaf bordar avf avr minimaxf minimaxr tideman
43.7660 44.1030 43.4060 44.1810 43.4080
43.2570 43.4000 43.5750 43.4000 44.0000 43.4100 43.5840
At risk of repetition... correctness of software is not
guaranteed.
CJC
On 27/09/2023 12:45, Colin Champion wrote:
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.
random fptp dblv seq conting nauru borda
sbc2 bucklin sinkhorn mj av coombs
12.5820 35.9910 - 45.8790 - 53.6880
80.5090 - 67.5170 - - 55.7040 69.1810
clower knockout spe benham btr-irv
baldwin nanson minimax minimaxwv minisum rp river
schulze asm cupper
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
condorcet+ random fptp dblv conting borda av
75.4610 75.5690 75.6860 75.8110 76.4530 75.8300
llull+ randomr fptpf fptpr dblvf contingr
bordaf bordar avf avr minimaxf minimaxr
75.8750 75.8660 76.2610 75.8330 76.2600
76.3780 76.2620 75.9250 76.2590 75.9530 76.2620
smith+ randomr fptpf fptpr dblvf contingr
bordaf bordar avf avr minimaxf minimaxr tideman
75.7640 75.7470 76.2310 75.7630 76.2400
76.4530 76.2530 75.8650 76.2420 75.9680 76.2470 76.0700
I will try a couple of other truncation models and then
look at strategic voting.
CJC
On 24/09/2023 13:41, Colin Champion wrote:
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.
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.
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.
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.
I will try to extend my own evaluation software to
allow a less restrictive model of truncation.
Colin
On 23/09/2023 02:47, Kevin Venzke wrote:
Hi Colin,
Le vendredi 22 septembre 2023 à 02:57:42 UTC−5, Colin Champion<colin.champion@routemaster.app> <mailto:colin.champion@routemaster.app> a écrit :
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.
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 intovotingmethods.net/calc <http://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 <http://votingmethods.net>
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