[EM] Re: Election-methods digest, Vol 1 #405 - 5 msgs

[Richard Moore]

Donald Davison wrote:
> The two methods [2-pass IRV or "Dan's Folly", and 2-winner 3-candidate IFPP or "Craig's Folly"]
 > have all parts exactly the same:
>     * They both use ranked ballots.
>     * They both are two seat election methods.
>     * They both elect the first candidate that has more than a quota.
>       While IRV does not have an official quota, in this case the
>       IRV first winner does win by more than what would be a quota.
>     * They both transfer all ballots of the first winner to the next
>       preferences.
>     * They both elect the next leading candidate after the transfer
>       as the second elected member.
> 
> The two methods are exactly the same, and being as we agree that one is
> `quite bad', it only follows that both are quite bad.  A bad method by any
> other name will still be bad.  Craig's Folly and Dan's Folly are two peas
> in a pod.

Can anybody spot the flaw in Donald's logic here? In fact all of 
Donald's statements are true, but he reached an unsupported conclusion.

This is a subtle non sequitur. In the fourth statement, Donald says 
"They both transfer all ballots of the first winner to the next 
preferences." This is true. However, the "first winner" is not always 
the same in both methods.

Consider the following case:

32: ACB
64: BAC
33: CBA

The first winner in IRV is C. C's first place votes transfer to B. The 
second winner is B.

The first winner in IFPP is B. B's first place votes transfer to A. 
The second winner is A.

> You don't need to be a `Gifted Mathematician' to understand the math of
> this logic.

I guess the irony of this statement is unintentional.

  -- Richard