[EM] Ordering defeats in Minimax

Fri May 12 06:36:27 PDT 2017

> On 08 May 2017, at 21:28, VoteFair <ElectionMethods at VoteFair.org> wrote:
> 
> On 5/7/2017 1:58 AM, Juho Laatu wrote:
> > ...
> > I think all Condorcet methods have a severe incentive to apply one
> > particular strategy. ...
> > ...
> > 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. ...
> 
> In real-world situations that involve more than about 10 voters, strategies do not work when Condorcet methods are used.

Yes, most strategic scenarios are difficult to apply and they may backfire. Or sometimes easy to apply but inefficient or harmless (e.g. incentive to rank all candidates). I note that if voters follow the advice to rank all potential winners, that makes strategy related questions somewhat simpler since we can expect to get lots of full rankings of all the potential winners. Just as you say, small elections with voters that know the opinions of each others are more problematic than large public elections with independent voters. Some societies might be more strategy oriented than others, but I hope people would soon learn that putting more effort on sincere campaigns works better than attempts to apply some strategy.

> 
> Based on my experience with the VoteFair American Idol poll, initially voters started out using approval-like voting, or single-mark-ballot-like voting.  But over time -- when they saw that the results revealed a full ranking and not just a single "winner" -- they learned to more fully rank the choices.  At that point the voters ranked choices at the same level only when they didn't have much of an opinion about which were better or worse than the others at that ranking level.

That sounds good. People may need some experiences or training to stat trusting new and better methods. Political elections are of course somewhat more competitive than polls, but I'd expect the same rules to apply also there.

> 
> So far I have not seen any strategy that works with Condorcet methods -- which I call "pairwise counting" when I'm talking to non-math folks. Yes, IF there is a cycle, or something close to a rock-paper-scissors-like cycle, then yes there are strategies that become relevant.

Yes, I have many times asked people to write generic guides (for Condorcet elections) that would tell the voters (or party strategists) when and how one should vote strategically. I have not seen any such working guidance yet. There are however some technically quite risk free strategies, like the idea to rank all the candidates in the hope of generating a loop that might have an effect, or strategy to give systematic guidance on how to loop the candidates of the opposing party, but also these are so far away from working strategies that they can not be considered an obvious vulnerability. Condorcet methods of course have the problem that always when there is a sincere loop, there is a majority that would like to change the winner. But making strategic decisions based on that before the election is far from easy. Considerations like "what if this particular group would have voted otherwise" are interesting to study after we know how people voted, but they are of no use before the election when we don't know who people are planning to vote, and what other strategies some other groupings might apply.

> 
> In the VoteFair American Idol polls the only times I saw a cycle were when just a few people -- say less than 20 -- had cast their vote, and by the time there were around 50 votes there was never a cycle.

Some polls may be more prone to having cycles than political elections. If we take 100 random candidates/options that voters do not know very well, and ask the voters to rank them, we might get loops because opinions of the voters would be quite random. In typical political elections there are strong voting patterns (e.g. left wing voters vote for the left wing candidates) that make such random loops less likely.

> 
> Plus, the ranking at around 50 votes typically was very close to the final ranking when a thousand or more ballots had been cast.

This is also a good sign, indicating that the results are stable.

Juho

> 
> Richard Fobes
> 
> 
> 
> On 5/7/2017 1:58 AM, Juho Laatu wrote:
>>> On 06 May 2017, at 23:26, Kevin Venzke <stepjak at yahoo.fr
>>> <mailto:stepjak at yahoo.fr>> wrote:
>> 
>>> It's not whether they are ranked (margins will essentially force me to
>>> rank
>>> them, I think), it's whether I decide to rank them sincerely.
>> 
>> 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.
>> 
>>> Legislators usually don't use election
>>> methods. I would say essentially they figure out among themselves what
>>> the outcome likely must be and then "elect" it, typically by a majority
>>> vote. If voters could do that directly I think that would be the ideal
>>> situation, as far as minimizing the need for strategy.
>> 
>> 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'm not sure if you thought I was talking about a legislature using
>>> Condorcet. What I was saying is that I don't think the behavior of a
>>> legislature would be emulated well by, for example, picking any arbitrary
>>> option from the top cycle. Some of those options may not be plausible
>>> outcomes, despite what the pairwise matrix says.
>> 
>> 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.
>> 
>>> >Yes, Plurality's reference to first preferences is not good. If one
>>> >wants to say something more generic that is not tied to first
>>> >preference votes, one should reformulate the criterion. The criterion
>>> >would not be as sexy that way. Also the use of implicit approval should
>>> >be made clearer, if the intention is to say something about voters that
>>> >assume it, or a method that makes some use of it.
>>> 
>>> 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 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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