ballotbox
Ballotbox is a java library of social choice rules. Here is the list of the social choice rules in this library.
The social choice rules are taken from the work of F. Aleskerov and
- Scoring Rules
- Plurality Vote
- Approval Voting
- Run-Off Vote
- Hare’s Procedure
- Inverse Plurality Vote
- Borda’s Rule
- Sum Vote
- Inverse Borda Rule
- Coomb’s Procedure
- Nanson’s Procedure
- Rules Using Majority Relation
- Rules Using Value Function
- Rules Using Tournament Matrix
- q-Paretian Rules
Scoring Rules
Plurality Vote
Each agent votes for its best alternative. If agent has more then one best alternative then one is chosen randomly.
Approval Voting
Each agent votes for its q best alternatives. When q = 0 only the best alternatives (even if there are more then one) are voted for. When q = 1 best and the second best alternatives are voted. Actually Approval Voting is defined as each agent can vote any number of alternatives from the top. When agents are humans q might be different for each agent.
Run-Off Vote
If a plurality vote cannot find a winner with majority then the best two alternatives are taken and a plurality vote is applied again to this two alternatives. To find the rest of the preference ordering, winner is removed from the list and the procedure is repeated until no alternative is left.
Hare’s Procedure
If there is no simple majority then the worst alternative is omitted and the procedure is repeated until there is a winner with simple majority. To find the rest of the preference ordering, winner is removed from the list and the procedure is repeated until no alternative is left.
Inverse Plurality Vote
The alternative which is regarded worst by the minimum number of agents is chosen to be the winner.
Borda’s Rule
Agents vote by scoring m-1 to the best alternative(s) and lesser amounts to the following alternatives. Where m is the maximum lower counter set cardinality. These values are added to find the winner and the ordering.
Sum Vote
Sum rule is a variant of Borda's rule. In this case agents vote with their scores that they have given to a particular alternative. These scores are added to find the winner and the ordering.
Inverse Borda Rule
At each round Borda's Rule is applied. The alternative with lowest score is omitted until only one alternative is left. To find the rest of the preference ordering winner is removed from the list and procedure repeated until no alternative is left.
Coomb’s Procedure
Alternatives which are worst by the maximum number of agents are omitted until there is a winner with simple majority. Ordering is made by removing the winners from the profile and repeating the procedure until no alternative is left.
Two implementations of this rule are made. First one uses the same simple majority count for all. Second implementation calculates simple majorities for only the agents that tests the alternative in question.
Nanson’s Procedure
Borda's Rule is applied and the alternatives with scores lower than the average score are omitted. The procedure is repeated until one alternative is left. The ordering is determined by the removal sequence of alternatives. Last removed is most preferred.
Rules Using Majority Relation
Winner(s) are found using minimal undominated set algorithm.
Condorcet Vote
Condorcet is also called majority relation. Pairwise comparison of every alternative is made for each agent. Results are stored in a directed graph (using jgrapht). This algorithm is designed to return two way edges for indifferent alternatives.
Fishburn’s Rule
A Condorcet vote is conducted and a directed graph where nodes are the alternatives is created. Edges in this directed graph are created if upper counter set of one of the nodes of the edge is a subset of the upper counter set of the other node in Condorcet result.
Uncovered Set I
Similar to Fishburn's Rule, a Condorcet vote is conducted and a directed graph where nodes are the alternatives is created. Edges in this directed graph are created if lower counter set of one of the nodes of the edge is a subset of the lower counter set of the other node in Condorcet result.
Uncovered Set II
A Condorcet vote is conducted and a directed graph where nodes are the alternatives is created. Edges in this directed graph are created if upper counter set of one alternative is a subset of the other alternative or equal; and alternative which is a subset beats the other in the Condorcet result.
Richelson Rule
A Condorcet vote is conducted and a directed graph where nodes are the alternatives is created. If a and b are two nodes of this directed graph and L(x) defines lower counter set of x and D(x) defines upper counter set of x then there will be an edge between a and b if
Rules Using Value Function
Copeland’s Rule Net
Condorcet vote applied and preferences ordered by (incoming degree - outgoing degree) of each alternative.
Copeland’s Rule Out
Condorcet vote applied and preferences ordered by outgoing degree of each alternative.
Copeland’s Rule In
Condorcet vote applied and preferences ordered by incoming degree of each alternative.
Rules Using Tournament Matrix
A tournament matrix is a matrix where columns and rows are alternatives. Value at (i, j) location of this matrix shows number individual preferences that i beats j.
Maxmin Procedure
The winner is found by taking first the maximum of the minimums of rows.
Minmax Procedure
The winner is found by taking the minimum of the maximum of columns.
q-Paretian Rules
Strong q-Paretian Simple Majority Rule
Where 
is the preference profile, I is a simple majority coalition and 
is set of all simple majority coalitions.
Strong q-Paretian Plurality Rule
Similar to strong q-Paretian simple majority but if several alternatives are choosen then their ordering will be made by counting the number of simple majority coalitions that selected them.
Strongest q-Paretian Simple Majority Rule
Where is the preference profile, I is a simple majority coalition and is set of all simple majority coalitions.
Ahmet Kutsi Nircan. 2006-07-16