[EM] round robin tournaments RBJ

[Juho Laatu]

It seems that quite typically different viewpoints on margins and winning votes are linked to the question of implicit approval. If someone votes A>B, does he say that his preference order is A>B>C=D=E or does he say that in addition to that he thinks that only A and B are acceptable and the other ones are not (as maybe in the example below?). This difference in interpretation may explain some cases where people seem to see different logic behind some ballot sets. I think the voters should be made well aware if their ranked vote is intended to carry also some implicit approval meaning (that may impact tho outcome of the election).

Majorities are also one point of interest. There are many majorities. Majority of citizens, majority of people with right to vote, majority of those that voted, majority of valid ballots and majority of those that took position in some particular question. In ranked ballot based elections one may end up having cyclic preferences, and in that situation some of the various majorities must be violated. It is not easy to say which ones one should violate. And the size of the "almost majority" on the other side may be of interest too. I also note that sometimes the easiest way out of this problem of violating some expressed opinions could be to elect the winner outside of the Smith set.

And of course if we take also strategic considerations and strategy regrets into account, then we will have a complex field of many fine-tuning level open questions.

I started my journey on Condorcet methods from margins and basic minmax. That seemed like the obvious first solution to the problem of how to vote in an as strategy free way as possible. Then I started wondering how the problems could be fixed using some other approaches and additions and fixes to the method. It seemed that one can try to patch one problem using some tricks, but since the problem of cyclic preferences did not vanish anyway, it seemed that whatever fixes one made, that led to somewhat more complex systems that also had their weak points that were now pushed to some new locations after trying to push the problems down in one place. Fixes in strategic performance easily led to poorer performance with sincere votes. So, the next question was if margins and minmax are anyway good enough. That method is anyway a very simple approach with some very natural properties and justification (one quite reasonable approach to measuring the level of opposition/support after the election, easy to understand counting process, ability to tell (in real-time) how close each candidate is to winning the race, = "required extra votes"). Why make the method any more complex if there is no clear need and if that introduces some new problems.

I also found that trying to establish a transitive preference order in the group preferences does not make sense. That's where I gave up with the Smith set criterion. It may not be easy to explain to a regular voter why someone outside the Smith set could be better than the insiders if someone draws a graph where the Smith set members are collected together in a group and the preference strengths between those candidates are not shown (or are shown as shorter arrows). But the target was anyway to find a fair method, not necessarily one that is easy to market.

One reason why I don't like implicit approvals very much is that they tend to bring some truncation incentive with them. It may be small enough not to matter in some situations, but in general ranked methods work as ranked methods only if people will sincerely rank the candidates. Bullet voting is not what I want. One can collect quite well sincere rankings (trying to be optimistic here) but not much more. Sincere rankings of special markers like "none of the above" are possible too.

One interesting question is if one could collect some more info from the ballots than what the pairwise comparison matrix does. One could identify e.g. true clones or closeness of being a true clone. But I'm not sure if one can benefit much from that. Also checking mutual majority would be one option. There are also other interesting questions, but still the basic question remains. Do all the additional tricks improve the very basic minmax with margins or do they just make the method more complex (maybe better in some places, maybe worse in others) and more like a hack instead of an agreed function that measures the quality of the candidates.

Juho


On 29.6.2011, at 9.39, Kevin Venzke wrote:

> --- En date de : Lun 27.6.11, robert bristow-johnson <rbj at audioimagination.com> a écrit :

>>> Anyway, a margins proposal is DOA, from the moment
>> anybody would point
>>> out the 35 A>B 25 B 40 C scenario. Does anybody
>> actually disagree with
>>> that? One's EM postings will have to be very, very
>> clever to persuade
>>> the media, public, etc., that A should win that race.
>> 
>> 
>> and even more clever to persuade me.  lessee...
>> 
>>    35 A>B
>>    25 B>A     A>B
>> by 10
>> 
>>    40 C>A
>>    35 A>C     C>A
>> by 5
>> 
>>    60 B>C
>>    40 C>B     B>C
>> by 20
>> 
>> looks like B wins to me.  why shouldn't he? 
> 
> B wins in WV (B's loss of 35 is weakest). A wins in Margins (A's loss of
> 5 is weakest).
> 
> Why shouldn't B win? I think it will be seen as a joke if A wins. The
> perceptible difference between A and C is that A got fewer votes and his
> supporters ranked a second candidate. It is hard to understand how this
> can make A a better outcome than C.
> 
> Maybe you can make the argument... But you probably have to deliver it
> to people lacking a lot of time and patience.
> 
> And I don't like a C win because there is a majority for B over C. If 
> C wins, then A and the A voters are being punished for their sincerity,
> when this scenario has no need to make anybody regret.
> 
>> (maybe because C's great defeat by B is not because B is so
>> great, but that C is Sarah Palin: gets a lot of hard-core
>> supports but a lot more of us know that she's a total
>> doofus.)
>> 
>> so maybe instead of Ranked Pairs or MinMax with margins (i
>> presume Schulze would also elect A), it should go to the
>> candidate in the Smith Set with the greatest winning margin
>> over any other in the Smith Set.  but it still should
>> be based on margins.
>> 
>> but it *is* an interesting problem.  Marcus, can you
>> comment?  Schulze beatpath method would also elect A,
>> no?  can you persuade us that A should win in this
>> scenario?
> 
> When you use margins, Schulze, Tideman, River, or Minmax all pick A.
> If you use WV with these, you get B.
> 
> Kevin Venzke
> 
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