Borda Count

The Borda count system assigns a score to each vote according to the following rule:

\[s = n - r + 1\]

where $s$ is the score, $n$ is the number of candidates and $r$ is the rank. Effectively, the score reverse codes the rank votes. The candidate with the highest Borda score is selected as the winner. As an example, consider the following:

The Borda scores for each candidate are:

which creates a tie between candidates b and c.

Example Usage

The following examples illustrate some ways in which the Borda system can be used in RankChoiceVoting.jl. To begin, let's generate some synthetic rank choice votes for candidates $C = \{c,k,m,n\}$ from 100 voters.

using RankChoiceVoting

data = [[:m,:n,:c,:k],[:n,:m,:c,:k],[:c,:k,:n,:m],[:k,:c,:n,:m]]
counts = [42,26,15,17]
rankings = Ranks(counts, data)
rankings = Ranks(data)

Ranks
┌────────┬──────────────────┐
│ Counts │ Ranks            │
├────────┼──────────────────┤
│ 1      │ [:m, :n, :c, :k] │
│ 1      │ [:n, :m, :c, :k] │
│ 1      │ [:c, :k, :n, :m] │
│ 1      │ [:k, :c, :n, :m] │
└────────┴──────────────────┘

Next, let's create objects for the Consistency criterion and the Borda voting system.

criterion = Consistency()
system = Borda()

Borda()

Compute Ranking

The function compute_ranks is used to generate a complete rank ordering of candidates. In the case of ties, candidates will share the same rank value.

compute_ranks(system, rankings)

([1, 1, 2, 2], [:n, :c, :m, :k])

Evaluate Winner

We can use the function evaluate_winner to return the winner of the election as a vector. If multiple candidates tie for winner, the vector will contain each winning candidate.

evaluate_winner(system, rankings)

2-element Vector{Symbol}:
 :n
 :c

Satisfies

The example below determines whether the a voting system is guaranteed to satisfy a given fairness criterion.

satisfies(system, criterion)

true

It is also possible to check whether a system satisfies a given fairness criterion for a specific set of rank choice votes.

satisfies(system, criterion, rankings)

true

In the case above, the Borda system satisfies the consistency criterion because it holds in general. However, if a system does not satisify a criterion in general, it may satisfy the criterion in specific cases.

Count Violations

The code block below shows how to use count_violations to determine the number of violations of a fairness criterion a given system produces for a specific set of rank choice votes.

count_violations(system, criterion, rankings)

0