[EM] cyclic preferences

[Forest Simmons]

I sympathize with the sentiments of those who would like to allow
expression of intransitive preferences.

In February of 1967 when I took "aptitude" tests after being sworn into
the US Army, I noticed that there were lots of questions of preference,
for example, one was,"Do you like working at a desk better than being
outdoors?"

It would be very easy to create a cycle in your answers to this multitude
of questions, especially if you enjoyed a variety of activities both
indoors and out, both mental and physical, both individual and team, etc.

I wondered if the Army would consider such a cycle as evidence of
irrationality or dishonesty (if they even checked for cycles).

To this day I don't know the answer, but I'm glad I made it home from
Vietnam relatively unscathed :')

As to whether allowing cyclic preferences would make comparisons of
methods easier, see below.

On Thu, 5 Aug 2004, Paul Kislanko wrote:

...

> My ideal ballot for a decision with more than 2 alternatives would have each
> pair listed and these choices:
>  X
>  Y
>  Either X or Y
>  Neither X nor Y
>
> When I've answered that question for every pair of alternatives, without
> inferring anything at all the counting system has collected what corresponds
> to a ranked ballot if you want to use IRV, a 1:1 mapping to the pair-wise
> results matrix if you want to use a Condorcet-style selection process, and
> if you're using approval it's very specific.
>
> When you get over a few candidates trying this with punch-outs would be
> messy, but either the electronic or #2 pencil version would be very fast and
> easy for the voter.
>
> My basic thought is that from a theoretical perspective it is worthwhile to
> divorce the preference-collection process from the vote-counting process.
> For one thing, it would make it a lot easier to analyze what the outcome
> would've been under different methods, and from a purely practical
> standpoint it would eliminate the sidebar discussions.
>

...

>
> >From a purely "academic" perspective, dividing an election method into its
> "collect data" and "count votes" components simplifies a lot of the
> comparative analysis. If the generalization of a ballot I suggested above is
> used, you infer a ranked ballot, with or without truncation and compare IRV
> to a Condorcet method that uses the derived ranked ballot and to a Condorcet
> method that uses the explicit pair-wise preferences of each voter. That
> would be a much more robust method, I'd think, since the same input would be
> used by all systems.
>

But different methods require different strategies, and different
strategies result in different data, i.e. different ballot markings, even
though the (blank) ballots are identical and expressive enough to
accommodate all of the different methods.

Consider the case of comparing Condorcet and Approval. With Kislanko style
ballots, even zero info strategy would result in different ballot markings
for the two methods: under Condorcet I might not feel the need to choose
the "Neither" or "Either" option, but under Approval (with more than two
candidates) I would have to use one or the other of these options
somewhere.

Forest