Election Bench

New Zealand votes on Saturday 7 November.

How this works

Polls 17 polls from 6pollsters, last 90 days The average Recent polls weigh most 2,000 runs Vote shares varied atrandom, as polls do,plus a typicalelection-day miss Seats under MMP Each party's middle 80%seat range Majority 62 of 122 seats Census 2023 65 general electorates,9 factors The 2023 pattern The 2023 vote againsteach factor, byelectorate The census boxes do not use the polls. Polls 17 polls from 6 pollsters, last 90 days The average Recent polls weigh most 2,000 runs Vote shares varied at random, as polls do,plus a typical election-day miss Seats under MMP Each party's middle 80% seat range Majority 62 of 122 seats Census 2023 65 general electorates, 9 factors The 2023 pattern The 2023 vote against each factor, byelectorate The census boxes do not use the polls.

Which electorates we assume each party wins

ACT: 2 electoratesGreen: 3 electoratesLabour: 27 electoratesNational: 36 electoratesTe Pāti Māori: 3 electorates

Why Parliament is not always 120 seats

A party keeps every electorate it wins, even beyond its share of the vote, so Parliament can grow: the Parliament page says which parties. A majority needs 62.

TOP

Parties near the 5% line

List seats need 5% of the vote or one electorate. Opportunity: 6.2%, 1.2 points above the line.

Proofs

The proofs cover every possible input to our models of the method but do not show the figures are right.

What we have proved

Seats

  • Every seat parties share out goes to exactly one party.

  • Party order never changes anyone's seats.

  • More votes never cost a party seats, for a fixed set of qualifying parties, if every other party's votes stay the same.

  • One more seat to share never costs a party a seat.

  • The vote threshold is applied exactly; votes for no party or independents earn no list seats.

  • Parliament grows only by electorates won beyond a party's share; list seats are never negative.

  • The majority line is the fewest seats above half of Parliament.

Coalitions

  • Every group in the Parliament page’s majority list has a majority, lost if any party leaves.

  • None is left out unless the list hits its length limit.

  • Fewest-party groups come first: no dropped group has fewer parties than a kept one.

Electorates

  • Every electorate has exactly one winner, whatever nationwide support does.

  • A general electorate changes hands exactly when the challenger gains more on the holder than the holder's lead.

  • If neither nationwide support nor support in polls of Māori-roll voters moves, Māori electorates keep the last election's lead.

  • If neither nationwide support nor Māori-roll polls move, no electorate changes hands.

  • More nationwide support never costs a party an electorate, if the party has some support and each Māori electorate's votes match its margin.

  • Our check flags assumed winners exactly when no nationwide shift yields them all.

Poll average

  • Leaving out undecided voters, averaged shares make up the whole vote before rounding.

  • Older polls never count for more than newer ones.

  • Moving support keeps shares totalling the whole vote, if no other party is pushed below zero and the other parties hold some support.

  • Ranges run low to high, within simulated results.

Simulation

  • Each run's election-day miss moves parties against each other, not the total, sized from past final-poll misses.

  • The starting spread's formula is exactly an even start updated by the combined polls.

Seat check

Our seat calculation gave the same seats as the proved version for the 2017, 2020, and 2023 results and 10,000 random cases, checked 17 October 2026.

Not proved

  • Whether 2,000 runs give steady figures; each update checks this statistically.
  • Display rounding: proofs use exact numbers.
  • Whether each calculation matches its proof: seats are compared directly; the rest are checked by tests, not proofs.

Checked by the Lean proof checker (Lean and Mathlib 4.34.1).