[EM] Highly-expressive preference voting

[Sebastiaan Snoeckx]

27/08/15 16:13, election-methods-request at lists.electorama.com:
>> This may sound like an insanely strange question, but I was wondering
>> whether there were specific election algorithms and ballot designs that
>> would allow a voter to express preferences between specific candidates,
>> without having to specify their preference between the expressions of
>> preferences themselves.
>>
>> Don't worry if this sounds inconsistent, I'll explain by example:
>>    1. The voter prefers A over B (A>B)
>>    2. The voter prefers C over D (C>D)
>>    3. The voter prefers E over F and G (E>F=G)
>>    4. The voter prefers their own preference of A>B over their preference
>> C>D, but could care less whether E>F=G is preferred over the others
>>
>> Notationally, it would be a bit like this: ((A>B)>(C>D))=(E>F=G)
>>
>> Ow! I can imagine any voting system choking over this (and imagine this
>> happening with loops allowed!), but it is an incredibly common thing in
>> real life: people prefer burgers over pizza and prefer coke over sprite
>> (YMMV!), but when you ask them wether this mean that they prefer burgers
>> over coke or pizza over sprite, they'll shrug and say these are not
>> comparable: (burgers>pizza)=(coke>sprite).
>>
>> In real-life elections, candidates are rarely comparable to each other
>> (ie. one-issue candidates or mutually-complementary ideologies), and
>> forcing voters to rank (or score, in a cardinal system) incomparable
>> candidates or ideologies seems to me like a lot of information is lost.
>>
>> Did this make any sense at all?
>>
>> I myself had been thinking this would be akin to a candidate-grouping
>> scheme (whereby candidates should be allowed to be part of multiple
>> groups, or none) where you'd have a matrix comparing every
>> group-candidate-ranking combination to every other
>> group-candidate-ranking combination. Or something in that style; or not.
>>
>>
>> Thanks and hoping to hear any and all comments!
 >>
>
> Dear Sebastiaan,
>
> Many years ago I designed with Forest a presomptuously called "Universal Preferential Ballot" that contained an approval cut-off between acceptable and unwanted candidates. Your example could not have been well represented. To obtain all the latitude you want to represent such details, I suggest you move to grade ballots:
> ((A>B)>(C>D))=(E>F=G)
> could become
> A: 100
> B: 49
> C: 12
> D: 9
> E: 51
> F: 0
> G: 0
>
> Of course, other interpretations are possible.
> Dr. Stéphane Rouillon
>

Yes, I was also thinking that graded ballots would be somewhat better, 
because you could give scores to the individual preferences, and the two 
equal groups ((A>B)>(C>D)) and (E>F=G) would have equal sums of preferences:

   A: 100
   B:  80
   C:  20
   D:  10
   E: 100
   F:  55
   G:  55

Note the sum of (A>B) is greater than the sum of (C>D), and the sum of 
((A>B))>(C>D)) is equal to the sum of (E>F=G) (ie. 210). Yet, the voter 
is still implying that B is better than F or G, which might not be true.

One could mathematically design their grades to be so, that all 
preferences and preference-orderings are accounted for, but you'd need 
to have a calculator and work backwards from the scores given to the 
groupings. Not really voter-friendly if you'd ask me...