Largest Remainder Method

Primary definition

A principle for converting votes into seats in List PR systems. After parties and groupings have been allocated seats in an electoral district because they have received full quotas (a) of votes, some seats will be unfilled, and some votes remain - for each party, less than a full quota (a). The remaining seats are then awarded to parties and groupings in order of the number of left/over votes they possess. The Largest Remainder Method tends to be more favourable to smaller parties than the alternative approach, the Highest Average Method.

Also known asHare-Niemeyer Method · Hamilton Method · Vinton's Method · Quota Method
1 sources cited4 related termsReviewed Aug 9, 2026
ACE Electoral Systems GlossaryView source
People also ask

What is the largest remainder method?

The largest remainder method is a proportional-representation formula that allocates seats using a quota. Parties or lists first receive the whole seats produced by dividing their votes by the quota. Any seats left over are then awarded in order of the largest unused vote remainders until all seats are filled.

How does the largest remainder method allocate seats?

The largest remainder method divides each party's vote total by a chosen quota, assigns the whole-number seats first, and records each party's remainder. If seats remain unallocated, they go to the parties with the largest remainders. The exact result can change depending on which quota formula the electoral law specifies.

What is an example of the largest remainder method?

For example, if four seats are allocated among several parties, each party's votes are divided by the prescribed quota. A party might earn one seat immediately and retain a large fractional remainder. After whole seats are assigned, the remaining seat or seats go to the largest remainders, subject to the system's rules.

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ACE

A principle for converting votes into seats in List PR systems. After parties and groupings have been allocated seats in an electoral district because they have received full quotas (a) of votes, some seats will be unfilled, and some votes remain - for each party, less than a full quota (a). The remaining seats are then awarded to parties and groupings in order of the number of left/over votes they possess. The Largest Remainder Method tends to be more favourable to smaller parties than the alternative approach, the Highest Average Method.

ACE Electoral Systems Glossary · 2024

Cite this term

Permanent URL · stable across revisions
Election Security Glossary. (2026). Largest Remainder Method. In Election Security Glossary. Retrieved August 20, 2026, from https://electionsecurityglossary.com/glossary/largest-remainder-method

Sources

1 cited · last checked Aug 9, 2026

01

ACE Electoral Systems Glossary
ACE Electoral Systems Glossary

Single-source

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