Approval Sorted Margins: Difference between revisions
Rearrange sections, minor wording, add GitHub reference
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There are two heuristics to implement Approval Sorted Margins: Sorted Margins (as stated above), and Marginal Ranked Approval Voting.
== Sorted Margins heuristic ==▼
Our goal is to rank candidates in a descending order such that each candidate pairwise defeats the next lower candidate. The first candidate in the ordering is the winner.▼
▲=== Preliminary assumptions ===
How you vote:
* A voter can rank all candidates and give more than one candidate the same rank. Equivalently, one can ''rate'' all candidates and give more than one candidate the same ''rating''. Then the candidate ranking may be inferred from the rates.
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* Rating a candidate 3 or above is considered approved (therefore ratings of zero, one or two are not approved), and giving one candidate a higher rate than another indicates that in a two-candidate race between the two, the voter would cast a vote for the higher rated candidate over the other.
* The default rating (or score, a term we will use interchangeably) for an unrated candidate is zero.
* A ballot will be considered invalid unless at least one candidate is rated
* Ballots are tabulated [[Condorcet_methods#Counting_with_matrices|as in other Condorcet methods]], into a Virtual Round Robin pairwise array. In such an array, the value A[X,Y] is the number of ballots giving a higher rating to candidate X than to candidate Y.
* Additionally, we also tabulate total approval for each candidate, resulting in a value of T[X] for each candidate X, with T[X] being the number of ballots that give an approved rating of 3 or more to candidate X. For convenience, we can store T[X] into the pairwise array location A[X,X], which would otherwise be unused.
▲== Sorted Margins heuristic ==
▲Our goal is to rank candidates in a descending order such that each candidate pairwise defeats the next lower candidate. The first candidate in the resulting ordering is the winner. If a Condorcet Winner exists they will be the first candidate in the order, and if a Condorcet Loser exists, they will be the last candidate in the order.
=== Approval Sorted Margins ===
As stated above, our goal is to create a ranking in descending order, in which every sequential pair of candidates X<sub>i</sub> and X<sub>i+1</sub> is in order pairwise. That is, candidate X<sub>i</sub>
* Initialize a ranking of all candidates in descending order of approval. That is, for any sequential pair of candidates X and Y in the initial ranking, T[X] >= T[Y].
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''(TODO: check and find examples)''
== References ==
[https://github.com/dodecatheon/approval-sorted-margins] GitHub python code that compares Approval Sorted Margins to other Condorcet methods with explicit approval cutoff.
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