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A positional voting system is a ranked voting method in which the options receive points based on their position on each ballot, and the option with the most points wins.

Donald G. Saari has published various works that analyze positional voting systems mathematically. The Borda count is the fundamental method that is explored by this analysis.

Other methods that don't use ranking can still this analysis by considering the vote as truncated preferences, and assigning equal rank points without needing to know the exact order.

Unranked methods that can be analyzed as positional systems:

• Plurality voting: First place receives 1 point, all other places receive 0.
• Anti-plurality voting: Last place receives 0 point, all other places receive 1.

And unranked methods for multiwinner elections: (N seat election)

• Single non-transferable vote: Same as plurality, one choice receives 1 point, others 0.
• Limited voting Less than N choices receive 1 point, all other places receive 0.
• Bloc voting : Up to N choices receive 1 point (for N seat election), all other places receive 0.

[edit] References

• Economic Theory, Vol. 15, Issue 1, 2000: Mathematical Structure of Voting Paradoxes: II. Positional Voting, DONALD G. SAARI

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