# ML Wiki

## Voting Theory

Voting Theory studies how to take individual rankings of voters and aggregate them to form the global ranking.

Examples:

• Votes for a president of a company/country, etc. All voters communicate their results and based on that the president is chosen
• Search engines: there are many results, how to show them?

## Notation and Relations

• let $A = \{a, b, c, ...\}$ be the set of candidates
• there are $N$ voters
• each voter can express his preference on the basis of a total order
• i.e. he has to rank all the candidates

For this notation we define the following relations (Voting Theory Relations)

• Weak and Strong Preference
• Indifference

## Voting Mechanisms and Principles

A voting mechanism (or voting procedure or voting method) takes a collection of votes (individual preferences of the candidates from set $A$) and forms the global ranking. Usually it choses a single candidate from the set $A$.

There are several voting procedures:

### Criteria

How to characterize "good" voting methods?

There are several criteria

PV 2PV Borda Cond.
Monotonicity
Solution Existence
Manipulation
Separability
Condorcet Fairness

Other principles: