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:

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

Envoyé de mon iPhone

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 08/27/2015 02:02 PM, Sebastiaan Snoeckx wrote:

A suitably altered version of Condorcet could do something like this.
Here's a simple (but probably impractical) example:

1. For each pair of candidates X, Y:

1.1. If the voter has already answered whether he prefers Y to X or X to
Y, skip.

1.2. Otherwise, ask the voter if he prefers X to Y, Y to X, or considers
them equal.

1.3. Then ask the voter his strength of preference from 0 to 1. Call
this preference intensity p.

1.4. If the voter preferred X to Y, let c[X, Y] = p, c[Y, X] = 0;
otherwise, let c[X, Y] = 0, c[Y, X] = p.

Once all voters have constructed their c-matrices, add the matrices up
and run the result through your Condorcet method of choice.

If the meta-preferences are ranked rather than rated, it gets trickier.
I imagine variants of say, Ranked Pairs would still work, though.
Something like:

when you determine whether to lock A>B, only count the voters whose
preferences for A>B are stronger than preferences that have already been
locked in or excluded.

Another option is to only consider stronger preferences and use weaker
preferences as tiebreaks. The reasoning would be: say that you're voter
X and have a strong preference for A>B and a weak for C>D, and say some
other voter Y has a strong preference for B>A and a weak for D>C. Then
it would be strange if his weak preference counts the same as your
strong one. Hence, only strong preferences should be considered at
first; then, if there are any ties, use the weak preferences. But
strategy might complicate the picture.

I think that's more like having a partial order, which is to say that
you know (about your own preferences):

A>B, B>C, but you don't know whether A>C.

This is very similar to the problem ranked voting tries to solve in the
first place, because you have something like:

voter X: A>B
voter Y: B>C

but you can't say anything directly about society's preference about
A>C. Society's preference might even be cyclical, as Condorcet cycle
examples show.

If the analogy is accurate, then the easiest way to deal with
burgers>pizza, coke>sprite would be to pretend that you're two
"mini-voters". These "mini-voters" would have weight 1/2 each (since
there's no reason the coke preference should override the burger
preference or vice versa), and they would vote:

mini-voter A: burgers>pizza
mini-voter B: coke>sprite

Note that they say nothing about the combined preference of burgers>coke
or pizza>sprite.
Similarly, say you were evaluating candidates on three different axes
(say defense, financial policy, and resistance to corruption), then you
could have three mini-voters who rank like this:

defense: A>B>C
economics: B>A>C
incorruptibility: C>A>B

That will leave it to the system how to extrapolate the social
preferences, which is the very purpose of that system :-) The system
would thus have more information to go on.

Note that if everybody does this, then you don't even have to scale the
power of the mini-voters, since each voter will have three different
mini-voters and thus equal power. In practice, though, you'd want to
scale the weight of each mini-voter so that different people with
different number of mini-voters each get the same power.