Issue Voting: a proposed voting method


Issue voting is a proposed voting method for electing a single winner among a set of declared candidates. It is defined as follows:


In this election, the number \(n\) of statements that each candidate must make is 5.

Candidate A: Dwayne Elizondo Mountain Dew Herbert Camacho

Candidate B: Fielding Mellish

Candidate C: Sheev Palpatine

A voter who supports Mellish and opposes Camacho and Palpatine can decide to approve all of Palpatine's statements and none of the statements of the other candidates. The ballot is: B1, B2, B3, B4, B5

Another voter might support more funding for public education and finds the other issues less important, or doesn't have opinions on other issues. This voter would approve the statement that promotes education regardless of the candidate, resulting in the following ballot: B3

A voter focused on a variety of issues more than a candidate might pick the following: A1, A5, B2, B3, B4, B5, C2, C3, C4, C5.

In this scenario with 3 voters, the results are:

Total for A (Camacho): 2

Total for B (Mellish): 10

Total for C (Palpatine): 4

Mellish gets elected with 10 votes. Palpatine comes in second with 4 votes and Camacho comes in third with 2 votes. These results can be expressed as a percentage of the maximum score obtainable, which is the number of statements per candidate (5) times the number of voters (3), which is 15 in this example.

Equivalence with range voting

This method is equivalent to range voting, where a voter can give from 0 to n points to any candidate. However, each point that a voter gives to a candidate is labeled with a statement or promise from the candidate.

For example, a candidate may decide to enter the same empty phrase, such as "I want a great president!", for each of their statements. In this case, the voter will simply score the candidate by checking some number of boxes for the candidate, regardless of what they say.

Benefits over approval voting or range voting

Requiring the candidates to make short, official statements shown on the ballots has the following advantages:

Usual advantages of range voting and approval voting:

Voter weight normalization

As in all forms of range voting including approval voting, the voter should give the maximum points to one candidate and the minimum points to some other candidate to have a maximum impact. This is probably obvious to most voters in the case of approval voting, not obvious in the general case of score voting, and perhaps even less obvious here where the voter is asked to vote on issues and may not want to support an issue insincerely for strategic purposes.

This problem can be solved by scaling the votes on each ballot, such that the maximum point difference between 2 candidates becomes the same for each ballot.

The voters in the earlier example cast the following ballots:

In the original formulation of the method, each approval results in 1 point. After normalization in which the difference between least-liked and most-liked candidates is set to 5, the points associated with each vote become:

Now voters automatically have a fair weight in the outcome of the election, without forcing them to vote for some issues insincerely.

Algorithm for counting a ballot:

  1. Determine the weight of the votes in a given ballot: Find x, the smallest number of votes that a candidate received. Find y, the largest number of votes that a candidate received. If x equals y, the weight is set to 1. Otherwise, the weight is set to 5/(y-x).
  2. The weight for each vote (instead of 1) is added to the total for each statement.

This normalization is useful for giving the same weight to each voter on which candidate will win the election, whether they vote sincerely or not. It is however not valid for reporting the percentage of approval for each statement, which should be done without normalization.

Practical issues

This method requires larger ballots than if only the candidate names and political party were shown. This is presumably not much of an issue, since statements would be bounded in length anyway.

Counting the votes with normalization is also slightly more complicated than in approval voting, but not by much.