Kevin's probably right. Here's another idea along the same lines that might lead somewhere: Safety Approval: Again ballots are ordinal with equal ranks and truncations allowed. For any set of tentative approval cutoffs, define a partial order on the set of ballots by saying that ballot X is safer than ballot Y iff ballot X gives tentative approval to someone that has more tentative approval than any candidate tentatively approved on ballot Y. Start by giving tentative approval only to the candidates ranked (equally) at the top. Then lower the tentative approval cutoffs on the least safe ballots (but not below the truncated candidates). Continue until each ballot that does not tentatively approve the current tentative approval champ tentatively approves all except its truncated candidates. The basic idea behind this method is that if your ballot approves only candidates near the bottom of the current approval list, then its approval cutoff is too risky. Note that for both this method and Fall Back Approval, if it turns out that all ballots end up approving all of their ranked candidates, then the result is equivalent to Approval, assuming that voters would rank only their approved candidates. If it turns out that some of the approval cutoffs end up above the lowest ranked candidates on some of the ballots, then the voters of those ballots would be pleasantly surprised. Forest From: Kevin Venzke <[EMAIL PROTECTED]> Subject: RE: [EM] Fall Back Approval To: [EMAIL PROTECTED] Message-ID: <[EMAIL PROTECTED]> Content-Type: text/plain; charset=iso-8859-1
Forest, --- "Simmons, Forest " <[EMAIL PROTECTED]> a �crit : > In the first round only the alternatives ranked first (or equal first) are > counted as approved, > i.e. a tentative cutoff is placed immediately below the top rank on each > ballot. > > In subsequent rounds the tentative cutoff is moved down one rank on all > ballots for which the > current tentative approval winner lies more than one rank below the current > tentative cutoff. > > When all tentative cutoffs cease to move, the current approval winner is > declared winner of the > election. > > [End of Method Definition] > > Is this method monotonic? > > Does it satisfy the FBC? I'm sure it lacks both. When a ballot approves a candidate (either initially or in response to a current leader), there is no guarantee that it will be purely helpful, since other ballots can "react" to it. This is similar to a method I suggested some time ago. I think the only difference is that in my method, *all* ranks above the current approval winner became approved. (Possibly I only suggested a three-slot version.) These "repeated rounds" methods (including, say, GIA) can't be monotonic, since they don't use information monotonically. (Kind of a silly thing to say, but it's an intuitive litmus test.) Kevin Venzke
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