[EM] Best Landau Method?
suzerainsimmons at outlook.com
Tue Jul 20 21:59:03 PDT 2021
For first approximation simplicity we temporarily ignore the possibity of pairwise ties in the following paragraphs ..
A candidate is in the Smith set if any other candidate can be reached from it by a beat path.
Similarly, a candidate is in the Landau set if any other candidate can be reached from it by a short beat path, meaning in only one or two steps. In that case it is said to be uncovered because no other candidate beats both it and every candidate that it beats.
Copeland is a well known monotonic method that always elects from Landau, for example.
Can you think of a Landau method that is both monotone and clone free? If so, you have excellent talent for this kind of work. Perhaps you could figure out a way to de-clone Copeland without messing up monotonicity.
The purpose of this message is to show you a succinct formulation of a Landau compliant method related to agenda based Sequential Pairwise Elimination. SPE methods are always Smith compliant, as well as monotone and clone independent to the degree the agenda is compliant in either or both of those ways.
An agenda for SPE is a list of alternatives in order of "promise" (presumptive merit, e.g. approval) from least to greatest. In SPE, at every step the pairwise loser of the two remaining least promising alternatives is eliminated until only one remains.
Let's call our new Landau compliant method APL for Agenda Processing Landau. Here goes ...
If the least promising alternative Z on the agenda covers the winner Y of APL applied recursively to the rest of the agenda, then elect Z, else elect Y.
That's the most succinct, complete definition possible of APL.
We can talk about it some more if there is any interest.
Sent from my MetroPCS 4G LTE Android Device
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