# Algo

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Algo

## 1. Voting

### 1.1. "one round"

1.1.1. Scoring rules

1.1.1.1. Borda

1.1.1.1.1. m-1,m-2,...,0

1.1.1.2. Plurality

1.1.1.2.1. 1,0,...,0

1.1.2. Approval

1.1.2.1. each candidate is voted on yes/no

1.1.2.2. max number of votes wins

1.1.3. Condorcet

1.1.3.1. pairwise election

1.1.3.2. N(i,j) > N(j,i) [fix i, for all j] => i wins

1.1.4. Maximin / Simpson

1.1.4.1. worst performance in all pairwise elections

1.1.4.2. min(N(i,j)) [fix i, for all j]

1.1.5. Copeland

1.1.5.1. N(i,j) > N(j,i) => C(i,j) = 1

1.1.5.2. N(i,j) = N(j,i) => C(i,j) = 0.5

1.1.5.3. N(i,j) < N(j,i) => C(i,j) = 0

1.1.5.4. sum(C(i,j)) [fix i, for all j] => score

1.1.6. Buckling

1.1.6.1. B(i,l) is number of votes, thank rank i in top l

1.1.6.2. l(i) is min(l) with l > n/2

1.1.6.3. max(l(i)) wins

1.1.7. Ranked pairs

1.1.7.1. establish order based on N(i,j)

1.1.7.2. starting with highest N(i,j)

1.1.7.3. lock in, move to next pair

1.1.8. Cup

1.1.8.1. balanced bintree

1.1.8.2. one leave per candidate

1.1.8.3. heap?

1.1.9. Scoring Approval aka Approving Scoring

1.1.9.1. range e.g. 1-X

1.1.10. Kemeny

1.1.10.1. minimizes number of inconsistencies

1.1.10.2. (if i > j there shall not be no j > i == inconsistency)

1.1.11. Slater

1.1.11.1. minimizes number of onconsistencies

1.1.11.2. pairwise election based

1.1.11.3. as few pairwise elections as possible

### 1.2. "two rounds"

1.2.1. Pluraility with runoff

1.2.1.1. all but 2 removed after first round

1.2.1.3. second round decides

### 1.3. "m-1 rounds"

1.3.1. Single transferable vote

1.3.1.1. lowest removed

1.3.1.2. votes transferred to next remaining