[EM] Need IRV examples; voting show

[Forest Simmons]

Rob here's an inconsistency example adapted from message 7642 of the EM
archives:

First Precinct:
                190 SHA
                140 HAS
                120 AHS

Second Precinct:
                150 SHA
                170 HAS
                230 AHS

According to IRV, candidate H wins decisively in both precincts,
but (according to IRV) candidate A wins decisively when the results from
both precincts are combined.


For the non-reverse symmetry example I like to beef it up to show how
blatant the violation is.  Otherwise one might argue that the violation is
just an artifact of a "circular tie."

40 AXCYB
40 BXAYC
20 CXBYA

Note that by Pareto  X strictly beats Y in the forward version and Y
strictly beats X in the reverse version, so there is no five way tie that
would allow B to win in both the forward and reverse versions in any
decent method.

Forest

On Wed, 30 Oct 2002, Rob LeGrand wrote:

> Howdy all,
>
> I'm developing an anti-IRV, pro-Approval presentation for the Travis
> County Libertarian Party's monthly Distinguished Speaker Series.  I'm
> looking for the best IRV examples that show nonmonotonicity and
> inconsistency.  For example, the one I plan to use for
> non-reverse-symmetry is
>
> 40%:A>C>B
> 40%:B>A>C
> 20%:C>B>A
>
> A good example will be as simple as possible (few candidates, few
> voting blocs) without seeming too unrealistic.  Any ideas for
> nonmonotonicity and inconsistency?
>
> Also, last night I stumbled across a one-hour educational special on
> voting methods.  It was part of a math series called For All Practical
> Purposes on the Annenberg/CPB Channel.  It used a convention of the
> imaginary Replacement Party to illustrate the differences among
> plurality and four ranked-ballot methods: plurality with runoff,
> sequential runoff (IRV), Borda and Condorcet.  The candidates were
> Mallory, Aberman, Richardson, Raupp and Valdez.  The final ballots were
>
> 18  12  10   9   4   2
> Ma  Ab  Ri  Ra  Va  Va
> Ra  Va  Ab  Ri  Ab  Ri
> Va  Ra  Va  Va  Ra  Ra
> Ri  Ri  Ra  Ab  Ri  Ab
> Ab  Ma  Ma  Ma  Ma  Ma
>
> Each candidate won under a different method.  It's a shame there was no
> mention of Approval, but it was a pretty good show.
>
> =====
> Rob LeGrand
> robl at aggies.org
> http://www.aggies.org/robl/
> for Texas State Representative, District 50
>
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