# [EM] Highly-expressive preference voting

Sebastiaan Snoeckx ikke at sebastiaansnoeckx.be
Mon Aug 31 14:09:49 PDT 2015

```30/08/15 00:46, James Kislanko <jpkislanko at bellsouth.net>:
>
> This example is a perfect demonstration of what I tried to describe a decade or so ago.There is no way to make a linear ordering of pairwise preferences if the voter uses different criteria depending upon what the pair is. I'd like my contribution to the pairwise matrix be based upon a ballot that gave "A or B, neither?" for every combination of choices.
>
>
>
> On Saturday, August 29, 2015 1:43 PM, Sebastiaan Snoeckx <ikke at sebastiaansnoeckx.be> wrote:
>
>
>   27/08/15 16:13, Juho Laatu <juho.laatu at gmail.com>:
>>> 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 candidatesshould 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!
>>>
>>
>>
>>
>> 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.
>>
>
> Yes, this is what I was thinking could be done to tally the results:
> consider these groupings (eg. "A>B") as "monolithic" in the calculation
> (thus behaving like a unique candidate) and then you'd end up, in an
> elaborate example, with something like this:
> ? 1. A>B
> ? 2. B>C
> ? 3. C>A
> ? 4. B
> ? 5. A>C
> ? 6. D>A
> ? 7. C>D
> ? 8. C
> ? 9. B>A
> ? 10. D
>
> On first sight, this would imply "A>B" to be the winner of the election.
> I'm sure there would be some advanced electoral mathematical algorithm
> available to check this, but does this *also* imply that, "A" *should*
> be the generalised winner, because obviously "A>B" implies that more
> people prefer A over B.
>
>> 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).
>>
>
> It's true that maybe in politics such a system isn't really needed, this
> would be more useful for highly specific, technical decisions.
>
>> 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).
>>
>
> I hadn't even considered such a use-case; it does seem like a good idea.
> Does anyone have examples of (real-life?) elections where this is
> allowed, and how then do they calculate the votes?
>
>> 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.
>>
>
> I'm not sure if I get your point here. Isn't a candidate grouping not
> the same as being allowed to equally rank candidates?
>
> Kind greetings,
> Sebastiaan
> ----
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>
>

There used to be a website, a clone of "Hot or Not", that used pairwise
matching of two faces, with the option to "skip" the current pairing.

That got me thinking: when implemented using "A or B or neither", isn't
this essentially a variation of Condorcet voting? Am I going crazy or is
that the simplest way of dealing with this sort of thing? The way you
phrase it certainly seems like it's exactly what I'm wondering about.

article on wikipedia:
<https://en.wikipedia.org/wiki/Potentially_all_pairwise_rankings_of_all_possible_alternatives>
(or the PAPRIKA method, as they call it) I had never heard of it before.
Now, without going into all the gory details of a method I'm not sure I
understand fully (and was surprised to see that someone went to the
actual trouble of implementing it), if all the *ranking criteria* are
well-defined (ie. all the candidates can be fully described with a fixed
set of properties), then it is mathematically possible to extract only
those pairwise matchings of interest, and then allow people to vote on
these.*

I have to admit, these kind of voting systems (or "decision-making
processes", but what's in a name?) seem to be more expressive than the
simple check/rank/score ballots, but it's still unclear how these must
be aggregated when you have more than one voter?

Am I still making sense?

-----
greetings,
Sebastiaan Snoeckx

* A weakness of this system is that voters also need to rank/score the
ranking criteria themselves, hence simply being a case of "it's turtles
all the way down."

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