[EM] Highly-expressive preference voting

Juho Laatu juho.laatu at gmail.com
Thu Aug 27 07:13:35 PDT 2015

```In many Condorcet methods votes are first added to a pairwise comparison matrix, and then the winner is determined based on that matrix. It would be straight forward to add also "partial" votes in the matrix. With "partial" (or "partial ranking") I mean votes that can rank A>B and E>F, but need not tell if A and/or B are preferred over E and/or F or vice versa. Also cyclic votes could be added in the matrix.

On the other hand I don't know who would like to cast a sincere cyclic vote. Strategic votes could be intentionally cyclic, but I guess we don't want to support that idea.

Also partial votes may not be needed. People should be able to rank all the candidates, or put them in random order or rank them equal if they can not decide. Do you have some good examples where partial votes would be seriously needed? Your food example (burgers vs. coke) works fine in foods, but I was wondering if this works also when electing one political leader or when selecting one policy (or is mandatory ranking of groupings a small enough problem to be ignored).

Theres's however one situation in my mind where partial votes could be useful. If we have multiple parties and each party has say 100 candidates, then it would make sense to be able to rank the strongest candidates of party A and strongest candidates of party B without having to rank all the 100 candidates of party A in order to tell that all party A candidates are better than any party B candidate.

This problem could be solved also by allowing the voter to rank various groups. We come back to your group-candidate-ranking from another point of view. Instead of casting a partial vote one could cast a vote that treats voters as groups. The aforementioned voter could vote A1 > A2 > PartyA > B1 > B2, where "PartyA" refers to all party A candidates except A1 and A2 (since they were ranked separately). This means that the voter ranks A3 and A4 equal, but worse than A1 and A2, and  both better than B1 and B2. If you want to have a partial vote (not taking position on if party A is better that party B), that could be e.g. (A1 > A2 > PartyA), (B1 > B2 > PartyB).

Juho

P.S. I sometimes proposed groupings in candidates lists or in the ballots as one solution to eliminating strategies from Condorcet style ranked methods. But I guess strategic voting is not of interest in this discussion.

> On 27 Aug 2015, at 15:02, Sebastiaan Snoeckx <ikke at sebastiaansnoeckx.be> wrote:
>
> Hello
>
> 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!
>
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