[EM] Modified Overall Preferences / margins, Smith set

[C.Benham]

On 10/07/2019 8:48 pm, Juho Laatu wrote:

> Concerning concrete examples with Losing Votes, similar examples seem 
> to serve as bad examples also with Losing Votes and Pairwise 
> Opposition (in addition to Winning Votes). I mean vote sets like 50: 
> A>B, 50:C>D, 1:D>*, where * refers to either A or B.
Juho, say * is A. Whereas my examples are simple and plausible yours are 
not.  Your example would be a bit more "realistic" if none of the pairwise
scores were identical, none of the first-preference scores were 
identical, none of the pairwise contests were exact ties and every 
candidate got some support
in every pairwise contest.

In your example three of the pairwise contests are 51-50 (A>C, D>A, 
D>B), A and C both have 50 first-preference votes, B and C tie 50-50 and 
B has no pairwise
support against A. Nonetheless  in your example I don't see how all 
three of Margins, Winning Votes and Margins not elect C (say with 
Smith//MinMax).

Chris Benham

>> On 09 Jul 2019, at 00:55, Juho Laatu <juho.laatu at gmail.com 
>> <mailto:juho.laatu at gmail.com>> wrote:
>>
>>> On 08 Jul 2019, at 22:05, C.Benham <cbenham at adam.com.au 
>>> <mailto:cbenham at adam.com.au>> wrote:
>>>
>>> 46: A>C
>>> 10: B>A
>>> 10: B>C
>>> 34: C=B
>>>
>>> B>A  54-46 (margin=8),   A>C 56-44 (margin=12),  C>B 46-20 (margin=26).
>>>
>>> Here on more than half the ballots B is voted both above A and no 
>>> lower than equal-top, and yet Margins elects A.
>>>
>>> No other candidate is voted at least equal-top on more than half the 
>>> ballots. Fans of Bucklin or any version of Median
>>> Ratings would be particularly incensed.
>>>
>>> The version of Losing Votes that I advocate elects B because it has 
>>> the 34C=B ballots give a whole vote to each of C and B
>>> in their pairwise comparison, so "C>B 46-20" becomes C>B 80-54, 
>>> giving B a winning MM Losing Votes score of 54.
>>>
>> I don't like losing votes too much since they may give strange 
>> results already with sincere votes. I don't have any dramatic 
>> examples available, but I believe there are such examples. I gave one 
>> example on winning votes earlier (50: A>B>C, 50: D>E>F, 1: F>A). 
>> Sorry about basing my claim on losing votes on "feelings only".
>
> P.S.
>
> Concerning concrete examples with Losing Votes, similar examples seem 
> to serve as bad examples also with Losing Votes and Pairwise 
> Opposition (in addition to Winning Votes). I mean vote sets like 50: 
> A>B, 50:C>D, 1:D>*, where * refers to either A or B.
>
> Winning Votes, Losing Votes and Pairwise Opposition are quite 
> artificial constructions when compared to margins and other such 
> pairwise comparison functions that aim more at estimating the (society 
> related) seriousness of each defeat. I discussed such more natural 
> pairwise comparison functions (e.g. Relative Margins and Moderated 
> Margins) a bit more in 
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2019-May/002126.html. 
> If one wants to change the behaviour of Margins, one option is not to 
> jump directly to Winning Votes etc but to make some less radical 
> changes (that avoid the worst pathologies). Also the MOP track is 
> interesting in the sense that the modification function can be used to 
> tweak the original (Margins or other) strengths in a similar manner 
> (e.g. based on indicated favourites as in MOP-F2).
>
>
>
>
> ----
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