Random ballot
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The random ballot voting method takes the one person one vote principle to an extreme by only counting the vote of one person. In an election or referendum, the ballot of a single voter is selected at random, and that ballot decides the result of the election.
The random ballot method is decisive, in that there is no possibility of a tied vote, assuming that the selected voter has expressed a preference (if not then another ballot can be selected at random). It is unbiased in that the probability of a particular result is equal to the proportion of total support that that result has in all the votes. It is also strategy-free in that there is no advantage in tactical voting.
But it is not deterministic, in that a different random selection could have produced a different result, and it undermines majority rule since there is a substantial possibility that the selected voter may be in the minority.
It is less a practical form of democracy and more a theoretical method designed to explain some of the properties of other voting methods, although it is occasionally used in real life as a tiebreaker for other methods.
This system has been advocated for use by US Law professor Akhil Reed Amar in his article "Choosing Representatives by Lottery Voting," 93(7) Yale Law Review (June 1984) 1283-1308 [1].
A related system was hypothesised by Isaac Asimov in his short story "Franchise" (1955: reprinted in Earth is Room Enough, Doubleday, 1957), where a single voter is chosen to decide each election. However, in Asimov's thought-experiment, the "elector" is not randomly selected, but chosen by computer to be as representative as possible of the populace at large. Asimov intended this story as a parody of opinion polling.
There is an element of randomness (other than tie-breaking) in some existing electoral systems, in two ways:
First, it is often observed that candidates who are placed in a high position on the ballot-paper will receive extra votes as a result, from voters who are apathetic (especially in elections with compulsory voting) or who have a strong preference for a party but are indifferent among individual candidates representing that party (when there are two or more). For this reason, many societies have abandoned traditional alphabetical listing of candidates on the ballot in favour of either ranking by the parties (eg, the Australian Senate), placement by lot, or rotation (eg, Hare-Clark STV-PR system used in Tasmania and the Australian Capital Territory. When candidates are ordered by lot on the ballot, the advantage of donkey voting can be decisive in a close race.
Secondly, in some Single Transferable Vote (STV) systems of proportional representation, an elected candidate's surplus of votes over and above the quota is transferred by selecting the required number of ballot papers at random. Thus, if the quota is 1,000 votes, a candidate who polls 1,200 first preference votes has a surplus of 200 votes that s/he does not need. In some STV systems (Ireland since 1922, and Australia from 1918 to 1984, electoral officials select 200 ballot-papers randomly from the 1,200. However, this has been criticised since it is not replicable if a recount is required. As a result, Australia has adopted a variant of fractional transfer, a.k.a the "Gregory method", by which all 1,200 ballot-papers are transferred but are marked down in value to 0.1667 (one-sixth) of a vote each. This means that 1,000 votes "stay with" the elected candidate, while the value of the 1,200 ballot-papers transferred equals only 200 votes.
