Algorithms & Models

Borda Count — How Ranked Ballots Become a Ranking

The Borda count asks every voter to rank all options, awards points by position, and crowns the best average — a consensus method with a famous strategic weakness.

Reviewed 2026 Updated only when the core methodology changes

What the Borda Count Is

The Borda count is a ranked-ballot aggregation method named after the French mathematician Jean-Charles de Borda, who described it in 1770. Each voter ranks the candidates; positions earn points; the candidate with the highest total wins.

It is the archetypal points-based ranking method — and the standard example in voting theory of the trade-off between consensus and manipulability.

What the Borda Count Ranks

The method ranks candidates in an election or poll from ordinal ballots — rankings, not ratings:

  • Political and organizational elections
  • Sports awards and polls (MVP voting, college polls)
  • Jury competitions where judges rank entries
  • Any setting where many ordered opinions must become one order

Core Inputs Used by the Borda Count

  • Ranked ballots — each voter orders some or all candidates
  • Point schedule — with n candidates, typically n−1 points for first place, n−2 for second, down to 0 for last (variants differ for partial ballots)

No intensities are measured: a first-place rank counts the same whether the voter adores the candidate or mildly prefers them.

How the Borda Count Works (High-Level)

The aggregation is pure addition:

  1. Convert every ballot’s positions into points.
  2. Sum each candidate’s points across all ballots.
  3. Order candidates by total — highest wins.

The result favors broad acceptability: a candidate who is everyone’s second choice can beat a polarizing candidate with more first-place votes but also many last-place rankings.

Conceptual model: Don’t ask who’s loved most — ask who’s ranked highest on average across everyone.

Key Properties

  • Consensus-seeking — rewards compromise candidates
  • Uses full ballot information — every rank of every voter counts
  • Violates majority criterion — a candidate with an absolute majority of first places can still lose
  • Violates independence of irrelevant alternatives — adding or removing a no-hope candidate can flip the order of the leaders

Update Frequency

The Borda count is computed once per election or poll — it is an aggregation rule, not a continuously updated rating.

Known Limitations and Criticisms

  • Strategic manipulation — voters can bury the strongest rival of their favorite at the bottom of the ballot, regardless of honest opinion (“ranking the rascal last”)
  • Clone sensitivity — nominating similar candidates can split or multiply points in ways that distort outcomes
  • Majority override — results can contradict the plain majority winner, which some consider disqualifying
  • Partial-ballot ambiguity — handling of unranked candidates changes results and invites gaming

Where the Borda Count Is Used

Borda-style points are used in:

  • Sports awards and rankings (e.g., MVP voting in several leagues, college football/basketball polls)
  • Some national elections (notably parliamentary elections in Nauru, and variants elsewhere)
  • Awards juries and society elections
  • The Eurovision Song Contest’s voting (a truncated positional-points relative)

Summary

The Borda count is ranking by consensus arithmetic: full ballots, positional points, highest total wins. Its elegance uses every opinion every voter offered; its weakness is that voters know it — and can aim their bottom ranks like weapons. Voting theory has spent two centuries living inside that tension.

References and Sources

  • de Borda, J.-C. Mémoire sur les élections au scrutin (1781).
  • Wikipedia. Borda count.
  • Saari, D. — analyses of positional voting paradoxes.