Comparison with other voting systems for participatory budgeting

On this page, we compare the Method of Equal Shares with some other voting systems that have been used by cities, or that have been proposed by academics or election reform advocates.

Comparison with the standard voting system

The voting system that is in use by almost every city selects all of the most popular projects, provided they fit in the budget limit. This is a "utilitarian method", in that it ensures an outcome that will (approximately) maximize the total "utility" of voters. In the computer science literature, this method is known as "utilitarian greedy". It is "greedy" because it proceeds one step at a time, and at each step selects the most popular projects without considering the impact of this decision on future steps.

Advantages of the standard method, when compared to the Method of Equal Shares:

• It is simpler and easier to understand.
• It leads to higher average voter satisfaction because it selects the most popular projects (but the satisfaction is less equally distributed).
• It tends to select only a small number of projects (which all have a high cost), making the implementation easier to administer.

Disadvantages of the standard method, when compared to the Method of Equal Shares:

• It cannot automatically handle geographic divisions of cities into districts and neighborhoods.
• Some voters have much higher influence on the outcome than others, which can be seen as unfair.
• Smaller cheap projects have a very low chance of being selected.
• Project proposers have an incentive to be wasteful because a project's probability of being selected is almost independent of its cost.
• Project proposers have incentives to "bundle" several projects into a big project, leading to outcomes that are worse overall.

Comparison with Majority Judgment in Paris

Paris used the standard voting system until 2019, allowing each voter to vote for 4-5 projects. In 2021, the city government switched to a system known as majority judgment. Under this voting system, each voter can grade every project (no limit on how many projects are graded). In Paris, there are four available grades:

• Favorite, I love it (Coup de cœur / J'adore)
• I like it, it's interesting (J'aime bien / C'est intéressant)
• Why not? (Pourquoi pas ?)
• I'm not convinced (Je ne suis pas convaincu.e)

Then, for each project, we compute the median grade, which is the grade such that half of the voters gave this or a higher grade, and half gave this or a lower grade. The city then selects the 2 projects with the highest median grade. (In large districts, it selects 3 projects.) Now, typically, the best projects all have a median grade of

"I like it, it's interesting". Thus, the city uses a tie-breaking scheme to actually make its decision, but city hall has never precisely announced what tie-breaking scheme it uses.

An advantage of majority judgment is that it allows voters to express a fine-grained view on each project, including a negative view.

A major disadvantage is that it may select projects that do not receive wide-spread support, as we will explain below.

The difference between popular projects and high-quality projects

The standard voting system used by most cities, and also the Method of Equal Shares, have as their aim to select projects that are popular: many people have voted for those projects, and thus we can assume that many residents of the city would be happy to see the project implemented. Thus, these voting systems allow the city to discover which projects have the broadest support in the population.

The philosophy underlying majority judgment (as used in Paris) is very different: it will select projects that are "high quality", in that for each project, a large fraction of voters who evaluated it agree that it is a good project. This is true even if many people do not care about the project and do not express an opinion about it. In particular, this could lead to the selection of projects that are only of interest to people living in the immediate area affected by the project, as we will now illustrate using an example.

Consider the following example, with two projects. For simplicity, assume that we only plan to select one winning project.

• Project 1 was graded by 2220 voters. 1000 of those voters (45%) gave it the highest grade
  , and another 550 voters (25%) gave it the second highest grade
  . Therefore, the median grade of Project 1 is the second highest grade
  .
• Project 2 was graded by 671 voters, many fewer than the 2220 voters who graded Project 1. Maybe this is the case because Project 2 is of very local interest, and people not living in the immediate area did not give Project 2 a grade. 400 of those 671 voters (60%) gave Project 2 the highest grade
  . Because that is more than half of the voters, the median grade of Project 2 is the highest grade
  .

The situation is depicted in the following graphic.

Majority judgment thus selects Project 2, because it has a higher median grade.

However, note that 1000 voters gave Project 1 the highest grade

, while Project 2 only got the highest grade from 400 voters. Thus, Project 2 is less popular. Depending on the preferences of the city government, it may view Project 2 as a bad use of money since it will satisfy many fewer residents.

In cities using the Method of Equal Shares (or even the standard voting method), Project 1 would be selected instead of Project 2.

Comparison with Quadratic Voting

Quadratic voting is intended to avoid strategic misrepresentations of preference intensity, and to thereby avoid a tyrany of the majority. With the Method of Equal Shares, both of these problems are addressed by its design of giving each voter an equal share of the budget to decide over. Thus, claiming to have intense preferences will principally influence one's own share of the budget, and a minority always has a share that cannot be taken away by the majority.

In principle, a quadratic voting interface could be combined with the Method of Equal Shares. But we expect that it is not worth using quadratic voting, given the added complexity for voters to understand and use the system.