[EM] IRV, SFC, WDSC examples

[MIKE OSSIPOFF]

I want to admit that I don't know whether or not Smith//PC fails
GSFC & SDSC. Since no one's proposing Smith//PC, it doesn't seem
important. But, aside from Tideman's other advantages, described by
Steve & Blake, Tideman(wv) & SSD have the big advantage over Smith//PC
that they've been shown to meet GSFC & SDSC. I don't want to discourage
Markus, or anyone, from proposing Smith//PC if they like it. I can't
guarantee its GSFC & SDSC compliance though.

I haven't yet succeeded in finding a GSFC failure example for
Smith//PC. Maybe it fails, maybe not. Maybe someone can show one way
or the other.

Anyway, it seems more relevant to show that IRV fails GSFC & SDSC.
In fact, as I said, IRV fails SFC & WDSC, and that means that
IRV fails GSFC & SDSC. I write, here, IRV failure examples for
SFC & WDSC. In addition to showing that IRV fails those criteria,
it serves to demonstrate the use of those 2 criteria:

GSFC:

100 voters. 3 candidates.

The criterion says that a candidate (whom I'll call "A") is SCW,
and that a majority vote him over B.

That means that the criteria specifies something about sincere
preferences & something about votes. My example complies with what
the criterion specifies, and an example-writer can configure everything
else as he wants to.

Sincere prefernces:

40: BAC
25: ABC
35: CAB

Votes: Voters vote exactly in accordance with their sincere rankings.

So: A is SCW, based on the sincere rankings. A majority vote A over
B. No one is falsifying a preference. The premise of the criterion is
met.

Now, what happens? A gets eliminated, transfers to B, and B wins.
The criterion says that B must not win. IRV fails SFC, and therefore
IRV fails GSFC too.

WDSC:

100 voters. 3 candidates.

All the criterion specifies is that a majority of all the voters
prefer A to B. My example complies with that, and anything else
not specified can be configured as I choose.

Sincere preference of 60 voters:

25: ABC
35: CAB

That's a majority who prefer A to B. I'll call them "the A>B majority".

Other people's votes:

40: BAC

(That's the actual voted ranking of the other 40 voters).

The criterion says that the A>B majority must have a way of making
B lose without any member of that majority reversing a preference.

How can they? For A to transfer to C instead of the B, his voters
would have to vote C 2nd--reversing the preference for B over C.

(Of course the A voters have no motivation to do that, but that's
beside the point).

The C voters could keep B from winning by insincerely voting A
in 1st place, over C. (That's what they'll feel forced to do in
actual practice). That means they're reversing their CA preference.

There's no way the A>B majority can make B lose without reversing a
preference. IRV fails WDSC, and therefore IRV fails SDSC.

Mike Ossipoff


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