How to deal with city districts?
Summary: Larger cities with several districts can choose to either hold separate PB elections for each district, or run a single city-wide election. We discuss the advantages and disadvantages of each approach.
Many larger cities run their participatory budgets using separate elections for each city district. Each resident can only vote for projects in their own district. The city assigns to each district a fraction of the overall budget (usually in proportion to the district's population), and the winning projects are computed separately for each district. Some cities in addition run an election involving just city-wide projects (projects that are not tied to a specific district). In that case, voters can vote twice: once for projects in their own district, and once for city-wide projects.
Other cities run a single city-wide election, where voters can vote for projects in any district. When using the standard voting method for participatory budgeting (which just selects the projects with the highest number of votes), this can have the unintended effect of spending very little money in some districts. But this effect does not occur when using the Method of Equal Shares.
On this page, we compare the two approaches. Both have advantages: running separate elections for each district guarantees the amount of money that will be spent in each district, and it could make voting easier for voters (since there are fewer projects to choose from). However, running a single city-wide election has advantages as well: it allows voters to vote for projects in any district, allowing voters to better express their preferences and thereby leading to better election outcomes. In addition, the voting method can optimally decide how much of the budget to spend on city-wide projects versus district projects.
Pre-dividing the budget among districts
By "pre-dividing" the budget, we mean that:
- a fixed budget for each district is set,
- every project is assigned to a district,
- the decision which projects win in a district are made without taking into account what happens in the elections in other districts.
Usually, voters are only allowed to vote for projects in their own district (or sometimes in two districts of their choice). Sometimes there is also a separate election for city-wide projects, again with a separate fixed budget set aside for city-wide projects. This election structure can also be used with the Method of Equal Shares.
A guaranteed amount of the budget is spent in each district
When pre-dividing the budget, the city can exactly control how much money will be spent on the projects of each district. This means that even small districts will see the desired amount of spending. It also means that even in districts with low turnout (that is, only a small percentage of residents coming to vote), the desired amount of money will be spent (even though the projects in that district get a small vote count).
It can be necessary to pre-divide the budget in cities where the districts are independently governed, and each district's budget is (partially) funded by the district government rather than by the city government.
Simpler for voters
In most cities that pre-divide the budget, voters are only allowed to vote for projects in their own district. Therefore, voters do not need to go through project proposals for other districts in order to identify any proposals that they would like to support. This reduces the difficulty of voting, and reduces the required time investment.
Voters cannot vote for projects outside their own district
As mentioned, typically voters are only allowed to vote for projects in their own district in cities that pre-divide the budget. However, voters may still have strong preferences over projects in other districts. This could arise, for example, when voters live close to the border of two districts, or if they send their children to school in another district, or they work in another district. Because voters cannot vote for projects in other districts, proposals that are attractive for many people across the city may not be funded by the participatory budget, because those projects do not have enough votes coming from only the district where the project is located. Thus, pre-dividing the budget can lead to worse election outcomes.
In addition, voters may be frustrated that they are not allowed to vote for projects they care about, just because they live in the wrong district.
Bad allocation of money between city-wide projects and district projects.
Several cities that pre-divide the budget run an additional separate election concerning city-wide projects that are not connected with a single district, and that may be of interest to residents of several districts. Those cities pre-specify the amount of money that will be spent on winning city-wide projects, and voters are allowed to vote both in their own district and for city-wide projects.
A problem with this arrangement is that there may be a district where many voters do not care strongly about the projects proposed for the district, but they do care strongly about some of the city-wide proposals. But because the budget is pre-divided between district spending and city-wide spending, the voting system cannot take these preferences into account. Thus, the city will spend a lot of money on relatively unpopular district projects, and not enough money on popular city-wide projects.
In 2021, in the Warsaw PB election, there were 2 project proposals concerning the same street: (A) new plants for Modlińska Street (a city-wide project), and (B) new pavement for Modlińska Street (a district project in the district of Białołęka). Project A received six times as many votes as B (12 463 vs 1 932). Even among the voters of Białołęka, A was twice as popular as B (4 365 vs 1 932). Project A was cheaper (435k vs 630k PLN). Even though A was more popular and cheaper than B, it was not selected (being a city-wide project) while B was selected.
Running a single city-wide election
An alternative is to simply run one single election containing both city-wide projects and projects for all the districts. Voters are allowed to vote for any of the projects, no matter which district they belong to. Doing this is not advisable when using the standard voting method for participatory budgeting (which just selects the projects with the highest vote counts). This is because projects of larger districts (with higher population) will tend to receive the most votes, leading to projects from smaller districts to lose.
However, the Method of Equal Shares can be used in this way, with just a single election. This is because the method, by design, gives every voter an equal share of the budget to decide over, and therefore larger districts are not advantaged over smaller districts. At the same time, because voters are allowed to vote for projects from across the city, the Method of Equal Shares may lead to better outcomes, since it can discover projects of interest to many voters across the city.
Voters can vote for projects outside their own district
Many city residents will have lives that do not only involve the district where they live, and instead they may spend plenty of time in other districts, such as the district where they work, where family and friends live, or where they go for recreation. In addition, if they live close to the border of two districts, they would naturally also have an interest in what happens in that nearby district. If we run a single election, voters can indicate their preferences for projects in all districts, allowing the voting rule to discover projects that have widespread support.
The voting rule can optimally decide how much to spend on city-wide projects
When pre-dividing the budget with a separate election for city-wide projects, the election planners need to decide what fraction of the overall budget to allocate to city-wide projects. But the optimum amount of spending on city-wide projects depends on voter preferences, and exactly how popular city-wide projects are compared to district projects. It could be that some of the city-wide projects enjoy very high support in the population, but cannot be funded because too little money was allocated to city-wide projects. On the other hand, in some districts there may be very popular projects in that district but that cannot be funded because too much money was allocated to city-wide projects.
In contrast, when running the Method of Equal Shares with one single election, it is not necessary to decide in advance how much money should go to city-wide projects. Instead the voting rule makes this decision based on the votes, and can thereby decide on an optimal split.
The voting rule can optimally divide the budget between districts
In some districts, many of the proposals for projects in that district may turn out to be unpopular, and the voters of that district instead would rather vote for projects in other (nearby) districts, or for city-wide projects. If we run a single election, voters can do this. In such cases, the Method of Equal Shares will decide to spend less money on the projects in districts where those projects are unpopular, and instead use the money for better projects. Note that this makes the voters of such districts more satisfied with the outcome.
In contrast, as we saw in an example discussed above, things can go wrong when pre-dividing the budget, because then some attractive and popular projects cannot be funded, because the pre-division of the budget turned out not to be optimal. Instead, weaker projects are funded.
Some districts may see little spending if not many of its residents vote
In some districts, a significantly larger fraction of residents will vote in the PB election than in others, for example because some districts have more politically interested residents, or more young residents who are comfortable voting in an online portal. Because the Method of Equal Shares gives all voters equal voting power, this means that districts with higher turnout will have more influence on the election outcome, and thus districts with lower turnout may see less spending than they would deserve looking just at the population counts. This could be seen as disadvantaging certain populations and districts. We discuss below a possible way to address this issue, by giving voters from districts with lower turnout a larger initial endowment.
Picture: Turnout by district in Warsaw
In the 2022 PB election in Warsaw, we can see that turnout varies from 3.2% of population in the lowest-turnout district to 10% of population in the highest-turnout district.
Thus, the highest-turnout district will have about 3 times as much influence per capita as the lowest-turnout district, if using the Method of Equal Shares without reweighting voters.
Some districts may see little spending if its voters prefer city-wide projects or projects in other districts
When discussing the advantages of having a single PB election, we mentioned that in districts where most project proposals are not very popular, money will instead be spent in other districts or on city-wide projects. This would be in line with voter preferences. However, it can also be seen as a disadvantage, if one views a district as deserving a proportional amount of the spending.
Voting for projects in all districts may be overwhelming for voters
When running a single election, voters can vote for projects in all districts. Thus, they can select from a potentially very large number of proposals, and it may be overwhelming having to go through all of them to make an informed decision. However, this issue can be addressed by designing the voting interface to make it easy for voters to filter the proposals, for example by allowing them to filter by district, or by allowing them to filter by project type (for example, "show me all the proposals for parks in my district").
Different turnout in different districts
The Method of Equal Shares assigns every voter an equal share of the budget. If different districts have different turnout rates (that is, a different percent of residents that actually vote), then this means that the total share of the budget assigns to a district is proportional to the number of voters in that district, not the number of residents of the district.
In situations where this is undesirable, the Method of Equal Shares can be adjusted to correct for the different turnout rates. This can be done by first deciding what fraction of the budget should go to each district (usually proportional to the district's population), and then dividing the district's share equally between the voters of that district. For example, if district 1 has a turnout rate of 5% and district 2 has a turnout rate of 10% (double), then each voter from district 1 would be assigned twice as much initial budget share compared to each voter from district 2.
The advantage of this reweighting is that districts with low turnout will not be underrepresented. However, there are also important advantages to not reweighting the voters. In particular, without reweighting, there is a larger incentive to participate for voters in low-turnout districts, and in particular it would incentivize districts to encourage their residents to vote. In addition, avoiding reweighting better follows the democratic "one person, one vote" principle.
We have complete voting data from the PB elections held in Warsaw. Warsaw pre-divides the budget and runs a separate election for city-wide projects. Using the voting data, we can simulate what would have happened if Warsaw had used the Method of Equal Shares instead. In particular, we can compare the outcomes of the two approaches we have discussed here: running Equal Shares in each district separately using a pre-divided budget, or running Equal Shares in a single election using the entire budget. For the latter, in the simulation, we reweighted voters as described above to correct for different turnout rates in different districts.
Our main finding is that under the single-election approach, a significantly larger fraction of the budget would go towards city-wide projects (compared to the fraction of the budget predetermined to go to city-wide projects by the City of Warsaw). In some districts, this effect is larger: a large fraction of the money assigned to the district is instead spent on city-wide projects, which would happen because voters in that district would prefer spending to go city-wide projects.
For the following pictures, we say that the "district budget" of a district is the amount of money assigned by the City of Warsaw to district projects. These budgets do not include the separate funds dedicated to city-wide projects. The following pictures show the fraction of the district budget that actually went to district projects (instead of going to city-wide projects). When we use the approach with pre-divided budgets (the maps on the left), the answer is always 100% (or in practice 99%), by design: the Method of Equal Shares is only allowed to spend the district budget on district projects. However, using the approach with a single election (the maps in the middle), we spend a significant fraction of the district budget on city-wide projects instead.