[EM] Re: IMHO, IRV superior to Approval

[wclark at xoom.org]

On re-reading, some of the definitions I mentioned seem unclear.

To clarify:

> (Def III:) A and X are clones iff they are both voted the same way,
> and all other options are voted the opposite way, on ALL ballots.

(Def IIIa:) A and X are clones iff every ballot that approves A also
approves X and disapproves all other options, and every ballot that
disapproves A also disapproves X and approves all other options.

(I didn't want anyone to think that the definition required all ballots to
be identical.)

Similarly for:

> (Def IV:) A and X are clones under Approval if they are both voted the
> same way (i.e. either both approved or both disapproved) on ALL ballots.

(Def IVa:) A and X are clones iff every ballot that approves A also
approves X, and every ballot that disapproves A also disapproves B.

> In any case, under II/III or IV, [Chris Benham's] Approval example no
> longer seems to hold.

For reference, I meant this example:

>> 01:A(9)>>X(2)>B(1)
>> 99:B(8)>A(7)>>X(1)

Of the two additional scenarios I mentioned:

> 01:A(9)>>X(2)>B(1)
> 99:B(8)>>A(7)>X(1)

> 01:A(9)>X(2)>>B(1)
> 99:B(8)>>A(7)>X(1)

...only the last one satisfies either (II/IIIa) or (IVa).

-wclark

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