I accept that the idea of limiting Dissapprovals is a mistake, but the example given by Kevin Venzke of a 2-candidate race being expanded to a 3-candidate race by the nomination of one of the first two's sister was not in my opinion good, (assuming the sister only takes votes from her brother) because any candidate with sufficient proportion of the votes to win a 2 -horse race will always win anyway. (BTW, I had noeone else's ideas in mind when I wrote "and not as joke". Maybe I meant "not as a good joke".)
So here in a (hopefully) more succinct form is the ammended version.
Voters number candidates in order of preference and also mark however many they like as Approved or Dissaproved . (There can be a little note on the ballot paper advising voters that handing out Dissaprovals increases the effect of their Approvals, and vice versa). If a candidate gets a majority of number 1s, he/she wins. Failing that, if one and only one candidate gets a majority of Approvals, he/she wins.
If more than one candidate gets a majority of Approvals, the rest are eliminated and their preferences are transfered. If that gives a candidate a majority, then he/she wins. If not the winner shall be the remaining candidate with the highest Approvals minus Disapprovals score.
If no candidate is Approved by the majority, and if there is one and only one candidate not Disapproved by the majority, then he/she wins. If more than one candidate is not Disapproved by the majority, the the rest are eliminated and their preferences transfered and so on as before.If that gives a candidate a majority, he/she wins.If not the winner shall be the candidate with the highest Approvals minus Dissapprovals score.
If all candidates are Disapproved by the majority, then the winner shall be the candidate with the highest Approvals minus Disapprovals score (unless you have a rule which states that in that case noone is elected).
Of course you could have a simpler version without the Disapprovals . Part of the idea is that I think that should be no need for any voter to strategise with his numbered rankings. It is highly likely if not certain it will elect a member of the Smith set, and of course it complies strictly with "Majority Favourite".
Thanks for taking some interest,
Chris Benham
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