On 28 Apr 2017, at 15:45, Toby Pereira tdp201b@yahoo.co.uk wrote:

I think I basically agree with Juho on this. The plurality criterion sounds like a reasonable criterion on the surface, but think about it more and it's arguably less so. To summarise, in a pairwise method, first place on a ballot doesn't hold any special status, nor does indeed last place (or joint last place or "unranked"). And a criterion shouldn't be used to impose an approval cut-off on a method that doesn't have one in its definition.

So while it sounds like a good criterion, removing the special status of these positions means that we are left with just saying that a candidate who pairwise beats another candidate should finish ahead in the overall ranking. Which is what all Condorcet methods do - except when there's a cycle.

Toby

From: Juho Laatu juho.laatu@gmail.com
To: Election Methods election-methods@lists.electorama.com
Sent: Thursday, 27 April 2017, 22:57
Subject: Re: [EM] Fwd: Ordering defeats in Minimax

First of all, my thinking when it comes to practical election methods is not very criterion oriented. I tend to see criteria and criterion compatibility as important theoretical results that are mostly too far from practical election method considerations to be applied directly on them as viability criteria. The relevance of different criteria to practical election methods is almost as low as the relevance of latest mathematical inventions to practical everyday economic calculations (well, not quite, but something in that direction). I'm about at the level of accepting Condorcet criterion if we seriously want to have a neutral majority based method for consensus oriented single winner elections. One has to take also into account the fact that all election methods are bound to break some potentially useful criteria. All this means that I classify Plurality and most other criteria as an interesting discussion points but not something to be followed categorically. There are many
criteria that are useful in the sense that most elections should have strong orientation in the described direction, but no need, or possibly with strong reasons to deviate from some criteria in some special (usually marginal) situations.

I think Plurality is a bit strange. Actually it is not even a criterion of of ranked methods. It is a criterion for ranked methods with implicit approval cutoff. It makes the assumption that a voter that casts a short vote has somehow approved those candidates that he marked, and not approved the others. In different elections the behaviour of voters with respect to which candidates will be marked on the ballot may vary a lot, and that may have nothing to do with how much the voters support or approve those candidates. In order to make any sense of the Plurality criterion we are thus tied to having an assumption of implicit approval in the ballots, where marking a candidate means approving that candidate at some level.

One reason why I don't like implicit approval in general (as a fact that is known by the voters) is that it encourages voters not to rank candidates that they don't like. Ranked methods work well only if most voters do rank explicitly at least all the potential winners (or all of them except one). If there is an approval cutoff, it would be better if it was an explicit one (this comment is not Plurality criterion specific but a general one).

Plurality criterion is a "heuristic" criterion in the sense that its message somehow sounds good (e.g. to people that do not regularly deal with election methods and their peculiarities). People would like also criterion "if voters would prefer A to B, then B should not win". But EM experts know that this criterion would not be a very good one, although it states something that we all would like to be true in all elections. What I'm trying to say here is only that we should be careful with cyclic group opinions. They will contain some nasty features. Instead of trying to pick a set of criteria that should be met 100%, my preferred approach is to see what kind of problems each method would be likely to face in real elections (typically but not necessarily large public elections with many different kind of voters that the strategists can not control), and evaluate them based on their performance in such real life situations.

I'm not well prepared to comment how margins can handle Plurality criterion but I'll address one basic (but theoretical and extreme, i.e. unlikely to happen in typical elections) example. 35:A, 34:B>C, 31:C. A has more first preferences than B has ballots where B is marked. B's worst defeat margin is however smallest (1), so it will win in typical margins based methods. Plurality criterion says that B should not win. B is however two votes short of being a Condorcet winner, so it can't be the worst of the worst. What if A would win? Plurality criterion pays special attention to A's high number of first preferences. But on the other hand voters would like to elect C instead of A with large majority (C>A voters would not be happy with the result). How about C then? Plurality criterion accepts C too, but using the high number of first preference votes of A as an argument that supports C does not make much sense. My conclusion is that this is a typical mess that we can get with c
ircular preferences. Our voters were quite stupid when they didn't sufficiently rank the potential winners. There are many different possible scenarios on what the truncated opinions might have been, and different results emerging from that. In this example my recommendation would be to tell to the voters that they should rank all potential winners (except maybe the worst one). I don't see any need to start blaming (or praising) margins on what happened. Maybe you have some realistic examples in your mind, that would give better justification to the Plurality criterion.

Juho

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That was a good summary of the weaknesses of the Plurality criterion.
I wonder if the Plurality criterion could be reformulated so that it
would not refer to the first preferences at all, and it would make its
message on the implicit approvals clearer.

Juho

One idea is that Plurality approximately says that if candidate X wins
then there should be some way to place approval cutoffs within the
rankings such that X is the approval winner. (First preferences come
into play because it's assumed no one would disapprove those.)

That's an interesting viewpoint. I'd like to see Condorcet tested in
some parliaments. Although negotiations and Plurality can be used to
solve many cases, also Condorcet and the idea of having multiple
candidates could have some benefits. The first one in my mind is
openness. Even when the "big boys" have agreed something behind the
screens, and then bring that decision into a majority vote, some smaller
groupings could add some alternatives in the election that they consider
better. This would open up the available alternatives to the world
(media, public), and all voters would have to take position on the
presented alternatives. Small parties or groupings could thus make
sensible compromise proposals that might even win, if they are good enough.

On 07 May 2017, at 12:39, Kristofer Munsterhjelm km_elmet@t-online.de wrote:

On 05/07/2017 10:58 AM, Juho Laatu wrote:

I think some parliaments use the following procedure for multiple proposals or amendments:

Some group decides the agenda (I'm not sure who; it probably depends on the parliament in question).

Then the parliament discusses the first two options, and does a majority vote between the two. It then does a majority vote between the winner so far and the next option, and so on until all options have been considered. The winner at the end of the procedure is the option that is accepted.

This method is Condorcet (because the CW beats everybody pairwise, and so whenever it becomes the winner so far, it'll stay the winner so far; and whenever it's the challenger, it will win against the winner so far and become the next winner so far). Furthermore, it's Smith. How cycles are broken depends on the agenda.

On 07 May 2017, at 13:32, Juho Laatu juho.laatu@gmail.com wrote:

Yes, this is some sort of "serial Condorcet".  The biggest problem of this approach is probably the agenda based cycle breaking that you mentioned.

If there is a Condorcet winner, it will win. But if there is any chance of having a cycle, then the chairman (if he decides the agenda) may arrange the agenda so that his favourite option is the last one in the queue of options. With three candidates this already determines the order of all pairwise votes.

With three candidates the cycle could be either A>B>C>A or A>C>B>A. The chairman wants A to win. The first vote will therefore be between B and C. If we have cycle A>B>C>A, B will win the first round, and A will win the second round (against B).  If we have cycle A>C>B>A, C will win the first round, and A will win the second round (against C). The chairman could thus pick the preferred winner in the case that there is no Condorcet winner.

The voters could also try to use some strategies. This gives us some quite interesting strategy patterns, since after the agenda has been set, the method is no more symmetric with respect to the different options. A and B supporters could also join forces and vote against A at the last round, if they don't like the chairmans idea of constructing a strategic agenda.

Juho

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I think all Condorcet methods have a severe incentive to apply one
particular strategy. That is the strategy of sincerity, or the strategy
if voting / casting one's vote. There is an incentive to rank all the
potential winners (one can rank them all by listing all except one of
them in the ballot).

All potential members of a top loop are included in the definition of
potential winners. Both sincere and strategic potential winners are
included in the definition.

Let's assume that in some group of voters all prefer A to B but they
don't rank candidates A and B. B wins the election, and A is not too far
behind. It is obvious that those voters would have had a better
strategy, the strategy of expressing their opinion on whether A or B
should win. This is not a rare incident if it is common among the voters
not to rank many of the potential winners. This could thus be the most
common mistake that a voter might make in an election. It is about as
severe as staying home in a Plurality election, and then wondering
afterwards, why the favourite of our group did not win.

Wouldn't you call this a strong strategic incentive? :-) The impact of
many other strategies could be much weaker and more improbable. Any
strategy that includes truncation would force you not to follow this
strategy. And strategies that include changing the order of some of the
candidates could be even more catastrophic. These effects are
particularly strong in large public elections where nobody has accurate
prior knowledge on how people are going to vote, or how much and what
strategies they might apply.

That's an interesting viewpoint. I'd like to see Condorcet tested in
some parliaments. Although negotiations and Plurality can be used to
solve many cases, also Condorcet and the idea of having multiple
candidates could have some benefits. The first one in my mind is
openness. Even when the "big boys" have agreed something behind the
screens, and then bring that decision into a majority vote, some smaller
groupings could add some alternatives in the election that they consider
better. This would open up the available alternatives to the world
(media, public), and all voters would have to take position on the
presented alternatives. Small parties or groupings could thus make
sensible compromise proposals that might even win, if they are good enough.

I think what I was thinking wast only that in small closed circles where
everyone knows everyone's opinions strategic tricks are easier (but not
easy) to apply than in typical large public elections.

I think Condorcet does pretty good job also when there are non-plausible
alternatives in the election. If some option is really bad, it would not
end up in the top cycle. Or do you expect strategic voting to be so
rampant that legislators would use their most disliked options in their
strategies and eventually elect them? A sensible voter should rank the
non-plausible non-wanted options last.

That's a good approach. Ability to win an Approval election (without
changing the rankings) says pretty much everything that the traditional
Plurality definition should say. Maybe it should be called and Approval
criterion or something like that instead (word "Plurality" is quite
confusing even with the original definition).

First preferences have an impact since they are the extreme top position
in the rankings. A good definition should however not include any
references to them. One viewpoint to this is that we can always add to
an election n new candidates where n = number of voters. Each voter has
now his own private candidate that is ranked first in one vote and last
in all other votes. The results should still be the same, although all
the old candidates now have zero first preference votes.

Juho

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On 08 May 2017, at 21:28, VoteFair ElectionMethods@VoteFair.org wrote:

On 5/7/2017 1:58 AM, Juho Laatu wrote:

In real-world situations that involve more than about 10 voters, strategies do not work when Condorcet methods are used.

Richard Fobes

On 5/7/2017 1:58 AM, Juho Laatu wrote:

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