User:Silvio Gesell/Tom's method: Difference between revisions
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How best to find the greatest stable $ is an open question. It is almost certainly economical to first check for a Condorcet winner. To do so by Tom's method, let $=∞. At $=∞, voters approve all candidates they prefer to last round's winner and disapprove all candidates they prefer last round's winner to (this will find the Condorcet winner or absence thereof in a maximum of N rounds without ties or 2<sup>N</sup> rounds with ties). In the absence of a Condorcet winner, the problem is potentially intractable, so it may be best to set a maximum search time (or number of rounds) in advance and, after ruling out a Condorcet winner, repeatedly eliminating any Condorcet loser (or candidate outside the Mutual Majority set, if one can easily be found), and finding the $=0 winner, "start the clock". First try $=1 and, thereafter:
If convergence succeeds, start over after doubling $ (if convergence succeeded last time) or setting it to the geomean of current and previous $.
If convergence fails, start over after halving $ (if convergence failed last time) or setting it to the geomean of current and previous $.
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