This page is an interactive companion to a forthcoming report titled Understanding How Proportional Representation Might Work in New York City. That report uses the results of the 2025 City Council elections to simulate two forms of proportional representation (PR) detailed in an earlier report, Reforming Big-City Elections. One of these, mixed-member PR (MMP), incorporates the current single-seat districts and allocates seats to parties in proportion to their vote shares using citywide “compensation seats.” The second, open-list PR, allocates seats to parties in proportion to their vote shares at the borough level. Seats then go to a party’s candidates in descending order of their vote totals.

Users of this website can adjust various features of each system. One is the number of compensation seats in MMP. In both systems, they also can decide which PR formula to use to allocate seats to parties: D’Hondt/Jefferson, which benefits larger parties, or Sainte-Laguë/Webster, which provides more overall proportionality of seats to votes (Gallagher 1991).

In addition, the site reports five indices of overall system performance. The Gallagher index describes overall seats/votes proportionality. Two more indices say how much fragmentation should be expected from the electoral system based only on its most basic design features. The two final indices say how much fragmentation there is in practice, given the observed votes.

This site is a project of Jack Santucci, Professorial Lecturer at the George Washington University and Part-time Lecturer at NYU Washington, DC. The Manhattan Institute generously supported its development.

The simulation data are available as two CSV files: borough_data_olpr.csv (used for the Open-List PR tab) and district-level_votes2.csv (used for the First-Past-the-Post and Mixed-Member PR tabs). The raw data and R code used to produce them will be available on GitHub following publication of the associated issue brief. The raw data were district-level returns (or borough portions for the four crossover districts) downloaded from the NYC Board of Elections on February 10, 2026.

Write-in candidates appear in the underlying data and are treated as follows. Because each write-in candidate received votes under a unique label, each is counted as a distinct party when computing the observed ENP(votes). Write-in candidates are excluded from the observed ENP(seats) and the Gallagher index, since they are ineligible to win seats, and they do not appear in any of the results tables.

Results for first-past-the-post are calculated from the district-level data. Thus the list of winners, their party endorsements, and any derivative measures may differ from the current situation (due, e.g., to vacancies, party switching, and so on).

Proportionality. Two indices describe how proportionally votes translate into seats. The Gallagher (1991) index summarises the overall gap between vote shares and seat shares across all parties; lower values indicate a more proportional outcome. The largest party seat share is a direct measure of how concentrated legislative power is in the leading party. For both indices, the app reports the observed value alongside the expectation from the Seat Product Model (SPM; Shugart and Taagepera 2017).

Fragmentation. Four indices describe how fragmented the party system is. The effective number of parties (ENP; Laakso and Taagepera 1979) is a standard measure that weights parties by their size; higher values indicate more parties sharing votes or seats in a meaningful way. The app reports observed ENP separately for votes and seats, alongside SPM-expected values for each (Shugart and Taagepera 2017). The SPM derives these expectations from the structural parameters of the electoral system alone—without reference to any election’s actual results—providing a benchmark against which observed outcomes can be compared.

The FPTP tab uses the simple SPM for single-tier systems (Shugart and Taagepera 2017). With all seats elected in single-seat districts, the mean district magnitude M = 1 and the assembly size S equals the number of districts. The seat product is therefore M × S = S. The expected values are:

• Largest party seat share: s1 = S^−1/8
• ENP(seats) = S^1/6
• ENP(votes) = S^1/4

With 51 single-seat districts, the expected ENP(seats) is 1.93 and ENP(votes) is 2.67.

The MMP tab uses an experimental version of the extended SPM for two-tier systems (Shugart 2024), which updates the version in Shugart and Taagepera (2017, eq. 15.2). The basic tier consists of the same 51 single-seat districts as under FPTP (M = 1). The tier ratio t is the share of the total assembly allocated as compensatory seats, which varies with the assembly-size slider. The expected values are computed as follows:

• Compensation coefficient: c = 1 − 0.38 × S_B^1/10
• Largest party seat share: s1 = (1 − t)^c × S_B^−1/8
• ENP(seats) = s1^−4/3
• ENP(votes) = (ENP(seats)^1.5 + 1)^2/3

where S_B is the number of basic-tier seats (always 51) and t = compensation seats ÷ total assembly size. When the slider is set to 51 (no compensation seats), t = 0 and the formula reduces to the simple FPTP expectation. Note that c depends only on S_B and is therefore fixed at 0.437 for this app.

Shugart (2024) notes that c typically falls in the range of 0.2–0.33 for systems with larger basic tiers. For this app, with a basic tier of only 51 seats—small by international standards—c computes to 0.437, which is somewhat above that range. This is consistent with the model’s logic: smaller basic tiers give compensation seats greater leverage, pushing c higher. Users should bear this in mind when interpreting the MMP expected values.

Note: the extended SPM for two-tier systems is still in development. The blog post about Wales (Shugart 2024) reflects the latest published thinking on it.

The ENP(votes) formula used here, N_V = (N_S^1.5 + 1)^2/3, is the general logical relationship between N_S and N_V developed in Shugart and Taagepera (2017). For the FPTP and OLPR tabs, where the simple SPM applies, this reduces to the approximation N_V ≈ (MS)^1/4.

The OLPR tab uses the simple SPM for single-tier systems (Shugart and Taagepera 2017), treating the five boroughs as the electoral districts. Each borough functions as a multi-seat district; the mean district magnitude M is the average number of seats per borough, and S is the total number of seats across all boroughs. The expected values are:

• Largest party seat share: s1 = (M × S)^−1/8
• ENP(seats) = (M × S)^1/6
• ENP(votes) = (M × S)^1/4

With a mean district magnitude of 10.2 seats and a total assembly size of 51 seats, the seat product is 520. The expected ENP(seats) is 2.84 and ENP(votes) is 4.78. Note that these values are fixed regardless of which allocation method is selected, since the SPM depends only on district structure, not on the allocation formula.

The number of seats allocated to each borough (its district magnitude, M) is determined as follows. First, the borough keeps all single-seat districts within its lines. Second, four of the original 51 single-seat districts straddle borough lines. For each such crossover district, the underlying data report vote totals separately for each borough’s portion of the district. The seat for that district is assigned to whichever borough contributed the most votes. Each borough then retains only the votes cast within its own portion of any crossover district. The resulting seat counts are: Manhattan 10, Brooklyn 16, Queens 14, Bronx 8, Staten Island 3.

Gallagher, Michael. 1991. “Proportionality, disproportionality and electoral systems.” Electoral Studies 10 (1): 33–51. https://doi.org/10.1016/0261-3794(91)90004-C

Laakso, Markku, and Rein Taagepera. 1979. “‘Effective’ number of parties: a measure with application to West Europe.” Comparative Political Studies 12 (1): 3–27. https://doi.org/10.1177/001041407901200101

Shugart, Matthew S. 2024. “What does the Seat Product Model say about the Welsh electoral reform?” Fruits and Votes (blog), June 27. https://fruitsandvotes.wordpress.com/2024/06/27/what-does-the-seat-product-model-say-about-the-welsh-electoral-reform/

Shugart, Matthew S., and Rein Taagepera. 2017. Votes from Seats: Logical Models of Electoral Systems. Cambridge University Press. https://www.cambridge.org/core/books/votes-from-seats/