# [EM] pairwise comparisons

Chris Benham cbenhamau at yahoo.com.au
Wed Apr 18 20:48:13 PDT 2018

```Curt,

Yes, an individual voter with cyclic preferences is confused and
inconsistent.

> Or is the Smith Set an accurate depiction of the electorate’s actual views?

In answer to that  question I would say accurate but not necessarily

Voters should be allowed to truncate and probably a lot of them will and
the cycle examples produced
by them doing so are much more plausible-looking to me than those where
all the voters rank all the
candidates.

6: A
5: B>C
3: C

A>B 6-5    B>C 5-3    C>A 8-6

All the candidates are in the Smith set.

Say we infer rating from ranking by interpreting ranking below no other
candidate as Top Rating and ranked above
at least one candidate as Approval. (I think many would find that
reasonable and natural.)

Top Rating scores: A6 > B5 > C3.     Approval scores: C8 > A6 > B5

B is positionally dominated by A and has the lowest approval score.

6: A
5: B
3: C

Assuming that we always elect A here (with all the voters truncating)
then electing B in the first example is a
failure of the Later-no-Help criterion, rewarding easy outrageous Burial
strategy.

Also electing B is a failure of the Plurality criterion, which says that
B isn't allowed to win because A has

Although B is in the Smith set no method I consider good or acceptable
will elect B.

MinMax (Margins)  elects B.

(Ranked Pairs, Beatpath and River are all equivalent to MinMax when
there are only three candidates.)

Chris Benham

On 19/04/2018 8:49 AM, Curt wrote:
> Hi,
>
> I’ve been chewing on some questions as part of exploring my views of ranked voting, and thought I would share here. For those of you who prefer not to think more philosophically about this, please excuse the missive. :-) But for the rest of you, I’m interested in your thoughts.
>
> Imagine a set of ten candidates, and one voter. The voter is asked to determine their views of these candidates. But instead of just being asked to rank them in order, the voter is asked to judge them pairwise.
>
> For six candidates, this means 15 questions. Each question being a comparison of A and B, with the voter picking their favorite of the two.
>
> First question, is it possible for a voter to generate a cycle? We know it is technically possible, trivially demonstrated. But is it possible that a voter, using some internal set of principles, would also generate a cycle? I would argue yes.
>
> If the voter does generate a cycle via these pairwise comparisons, what does this mean? Does it mean the voter is confused? Does it mean the voter is inconsistent? Does it mean that this cycle or cycles are an accurate depiction of the voter’s actual views?
>
> Say that we then ask the voter to create an actual ranked ballot out of these ten candidates, and the voter manages to do so. What happened in that process of the voter deciding the rankings? Was it a clarifying experience? Did the voter’s preferences change? Did the voter compromise? Did the voter lie?
>
> And finally, say that a collection of these voters submit their ranked ballots (not just their pairwise comparisons), and the votes are tabulated, and the result is a three-candidate Smith Set, where each candidate defeats all other candidates outside the Smith Set.
>
> What does that Smith Set mean? Is the electorate confused? Is the electorate inconsistent? Or is the Smith Set an accurate depiction of the electorate’s actual views?
>
> Thanks,
> Curt
>
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