Maximum Constrained Approval Bucklin: Difference between revisions
Maximum Constrained Approval Bucklin (view source)
Revision as of 10:43, 15 March 2022
, 2 years agoTypography: <math>-ify indexed variables
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== Determining the support for X ==
Let <math>r</math> be the rank and round number, <math>n</math> the number of candidates so far, and <math>c_k</math> the kth elected candidate. Consider unranked candidates to be ranked equal below every explicitly ranked candidate, i.e. never approved in any round. The linear program for determining the support of candidate X as (n+1)th candidate is:
maximize: sum over all voters v: support[v][n+1]
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(sum over i = 1 ... n+1: support[v][i]) <= v's initial weight
where <math>c_
The three clauses do the following:
# imposes the Droop constraint: that any elected candidate <math>c_i</math> must have more than a Droop quota's worth of approvals according to the implicit approval cutoff for round r.
# defines support: <math>c_i</math>'s support is the number of voters who rank <math>c_i</math> at or above rank <math>r</math>.
# defines each voter's budget: no voter can spread more support across the candidates than his ballot's initial weight. The initial weight is 1 per voter for ordinary elections, or some other value in case of a weighted vote.
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