Candidates listed first on the ballot have a small but measurable advantage. So some jurisdictions print...

 

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Candidates listed first on the ballot have a small but measurable advantage. So some jurisdictions print the names on the ballot in every possible order. An election has seven candidates. Three are Pastafarians, two are Socialites, and one is from the Monster Raving Loony Party (MRLP - that is the name of a real party in Great Britain!). a) How many ways are there to select a non-empty subset of all candidates (order does not matter)? (This would be relevant if you want to examine all possible coalitions for the purposes of Banzhaf power). b) How many ways are there to print first the Socialites, then the MRLP candidate, and the Pastafarians last? (This comes up if the Socialites and MRLP are a winning coalition in the Banzhaf sense, MRLP is critical, and you want to figure out how many sequential coalitions correspond to this winning coalition where the Monster Raving Loony Party is the pivotal player). Here would be an example of such a ballot. (S1, S2, MRLP, P2, P1, P3). You are supposed to find all possibilities. Candidates listed first on the ballot have a small but measurable advantage. So some jurisdictions print the names on the ballot in every possible order. An election has seven candidates. Three are Pastafarians, two are Socialites, and one is from the Monster Raving Loony Party (MRLP - that is the name of a real party in Great Britain!). a) How many ways are there to select a non-empty subset of all candidates (order does not matter)? (This would be relevant if you want to examine all possible coalitions for the purposes of Banzhaf power). b) How many ways are there to print first the Socialites, then the MRLP candidate, and the Pastafarians last? (This comes up if the Socialites and MRLP are a winning coalition in the Banzhaf sense, MRLP is critical, and you want to figure out how many sequential coalitions correspond to this winning coalition where the Monster Raving Loony Party is the pivotal player). Here would be an example of such a ballot. (S1, S2, MRLP, P2, P1, P3). You are supposed to find all possibilities.