# Description of the voting algorithms

Here's a description of the voting algorithms used by Rangepoll

### Common voting example

Here are the collected results for a vote for the best fruits:

Voter Apple Cherry Pear
Alice 2 3 1
Bob 1 3 2
Cindy 4 1 5

## Max

This is the simplest and most intuivite voting algorithm.

In this algorithm, the sum of each vote is computed and the winner is the highest ranked choice

Giving, in the example above:

• Apple: 7 points
• Cherry: 7 points
• Pear: 8 points

This algorithm is the only one allowing multiple choice to have the same vote.

This type of vote suffers from bipolar voters (those who vote with 1 or 5 but not in between) since the vote 5 has a lot more weight than note of 1

## Bordat

This algorithm is similar to Max algorithm above except that it is first ranking the choices for each voter and fixing notes to the rank order

In the example above, Cindy's vote would be sorted and ranked

• Apple: 2 (instead of 4)
• Cherry: 1 (instead of 1)
• Pear: 3 (instead of 5)

Then summing the votes gives this result:

• Apple: 5 points
• Cherry: 7 points
• Pear: 6 points

## Binary

A simple Yes/No voting.

This is like Bordat algorithm with only two choices (1: No and 2: Yes).

It's probably more interesting to check the poll's file after voting to have a list of voter and their vote.

Not applicable for the example above

## Condorcet

This algorithm compares each choice for all voters to other choices and rank them based on the number of time they win

In the example above, such comparison would yield

• Apple vs Cherry: Wins 1 time (for Cindy), looses 2 times (for Alice and Bob) => Lost
• Apple vs Pear: Wins 1 time (for Alice), looses 2 times (for Bob and Cindy) => Lost
• Cherry vs Pear: Wins 2 times (for Alice and Bob), fails 1 time (for Cindy) => Win

Then summing the votes gives this result:

• Apple: Win 0 times (neither against Pear nor Cherry)
• Cherry: Win 2 times (against Pear and Apple)
• Pear: Win 1 time (against Apple)

This algorithm can lead to a tie.

The main reason for using this algorithm is to select the best concensus among voters.

## First choice

This algorithm extracts the first choice for each voter and only sum them

In the example above, such extraction would yield

• Apple: 0 first choice
• Cherry: 2 first choices (Alice and Bob)
• Pear: 1 first choice (Cindy)

This algorithm is likely to give ties if the number of voter is small compared to the possible choices