D'Hondt method

D'Hondt method is a highest-averages apportionment method for allocating seats in parliament among competing political parties, in proportion to the number of votes each one received.

Idea

Most parliamentary systems that use proportional representation need a deterministic way to turn vote counts into a table of seats, one that stays proportional without producing fractional seats. The D'Hondt method solves this with repeated division: it hands out seats one at a time, always to whichever party currently "deserves" the next seat most.

This project implements the method as a small browser tool, with an optional preset for Serbia's parliamentary election rules including an electoral threshold and an exemption/multiplier for national minority parties.

Method

Let there be $p$ parties competing for $s$ seats, where party $i$ received $v_i$ votes.

For $s$ rounds, and for every party $i$ still in the running, compute the quotient: $$q_i = \frac{v_i}{n_i + 1}$$ where $n_i$ is the number of seats party $i$ has already been awarded. The seat for that round goes to whichever party has the highest $q_i$, its seat count $n_i$ is incremented, and the process repeats until all $s$ seats are allocated.

If two parties tie on quotient, the party with more raw votes wins the seat.

Before the quotient rounds run, a party can be excluded (its votes never enter the calculation) if it falls under an electoral threshold.

Additional rules

Many countries that use D'Hondt method implement their own set of subrules. For now, only the rules used in Serbian Parliamentary elections are implemented.

Serbia preset

• Parties need 3% of the total votes cast to win any seats (editable in the UI, since thresholds vary by country and by election).
• The threshold is measured against all votes cast, invalid/blank ballots included - not just the sum of party votes.
• Parties representing national minorities are exempt from the threshold, and their votes are multiplied by 1.35 before seats are allocated.

About

This is a static, dependency-free web app build using plain HTML, CSS, and JavaScript. Given a list of parties and their votes, it:

• runs the D'Hondt allocation above and shows the resulting seats per party,
• displays a semicircular hemicycle chart of the resulting parliament,
• reports vote share, seat share, and (optionally) turnout, once "registered voters" and/or "total votes cast" are filled in,
• lets you step through the calculation round by round in a quotient table,
• switches between a Basic mode (custom threshold, no special rules) and a Serbia mode (threshold + minority-party rules) via a mode toggle.

Running the program

You can run the simulation by visiting the following link

Future updates

Future updates of this project will focus on implementing the rules found in other legislatures and additional country-specific presets.