Smith/<something IBI> at least has the benefit of satisfying later-no-help ...
I'm afraid not. IBIFA fails Later-No-Help because adding a lower (or "later") preference (i.e. rating another candidate X
above Bottom) can trigger another (say a second) round that is won by a candidate (not X) you prefer to the one (also not X)
who would have otherwise won (say in the first round).
I thought of a possible kludge to try and fix that but it makes the method much more complicated and and less Condorcet
*(Say we are using 3-slot IBIFA.) We consider the IBIFA winner A to be provisional. Then we truncate all the ballots below A
and if A is still the IBIFA winner we elect A.
But if instead there is a new IBIFA winner B, we un-truncate the ballots below A and truncate below B and if B is still the
IBIFA winner then we elect B.
But if instead there is a new IBIFA winner C then repeat the process. If we run out of candidates or a previous provisional
winner appears, then we simply elect the most approved candidate.*
A very ugly answer to a question no-one was asking, and I'm not even completely sure it works. Median Ratings methods
(such as Bucklin and MJ) do meet Later-no-Help. Arguably it is desirable that Later-no-Help and Later-no-Harm should
either both be met (like IRV) or both failed (like IBIFA and Condorcet methods). Otherwise you either get a random-fill
incentive (yuck) or a very strong truncation (or only use the top and bottom rating slots) incentive.
And complying with Later-no-Help is one of the properties that Woodall has proved is incompatible with Condorcet, so
"Smith/ anything" can't meet it. The other criterion compliances in the same boat are Later-no-Harm, Particpation,
Mono-raise-random, Mono-raise-delete, Mono-sub-plump, Mono-sub-top.
On 20/06/2019 5:20 am, Ted Stern wrote:
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