Random ballot

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The random ballot, single stochastic vote, or lottery voting is an electoral system in which an election is decided on the basis of a single randomly selected ballot.

It is closely related to random dictatorship;

].

Method and properties

In an election or referendum, the ballot of a single voter is selected at random, and that ballot decides the result of the election. In this way, each candidate or option wins with a probability exactly equal to the fraction of the electorate favouring that candidate or option.

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

.

Emergent properties

See also:

emergent property

If the random ballot is used to select the members of a multi-constituency body, it can serve to retain the attractive features of both

.

As the winner of each ballot is chosen randomly, the party with the largest vote share is most likely to get the greatest number of candidates. In fact, as the number of ballots grows, the percentage representation of each party in the elected body will get closer and closer to their actual proportion of the vote across the entire electorate. At the same time, the chance of a randomly selected highly unrepresentative body diminishes.

For example, a minority party with 1% of the vote might have a 1/100 chance of getting a seat in each ballot. In a 50-person assembly, the probability of a majority for this party being chosen by random ballot is approximately (using the binomial distribution CDF)

${\displaystyle \sum _{k=0}^{24}{50 \choose k}\left({\frac {99}{100}}\right)^{k}\left({\frac {1}{100}}\right)^{50-k}=I_{1/100}(26,25)\approx 10^{-38},}$

This is a vanishingly small chance, which negates the possibility of small parties winning majorities due to random chance.

At same time, the random ballot preserves a local representative for each constituency, although this individual may not have received a majority of votes of their constituents.

Prevalence

There are no examples of the random ballot in use in practice, but as a thought experiment,^[5] it has been used to explain some of the properties of other electoral systems, and it is occasionally used in real life as a tiebreaker for other methods.

Randomness in other electoral systems

There are various other elements of randomness (other than tie-breaking) in existing electoral systems:

1. Randomly ordering candidates on a list.. 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

can be decisive in a close race.

2. Randomly selecting votes for transfer. In some

", by which all 1,200 ballot-papers are transferred but are marked down in value to 0.1666 (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.

3. Randomly selecting winners. This method is called sortition: rather than choosing ballots, it chooses candidates directly by lot, with no input from the voters (except perhaps a nominating or screening process). This is not the same as random ballot, since random ballot is weighted in favor of candidates who receive more votes. Random ballot would behave identically to random winner only if all candidates received the same number of votes.

References