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In a democratic election, the winning side is the one that gets the most votes 鈥� at least, normally. A test of alternative voting systems has found that in some cases, it is actually possible to increase overall satisfaction by delivering a result聽in which a minority decision prospers.

Alessandra Casella of Columbia University and Luis Sanchez of Cornell University in New York tested two voting systems in a survey ahead of a state-wide Californian ballot in 2016.

Rather than one vote per person, the systems 鈥� known as storable and quadratic votes 鈥� give people multiple votes to allocate to a range of issues. 聽鈥淭he ingenuity of the voting schemes is that they induce the voter to reveal her priorities sincerely,鈥� says Casella.

The researchers asked 600 California residents about four issues that were likely to be included on the ballot. They selected issues that were unlikely to result in a landslide, but about which some voters would feel strongly 鈥� such as requiring law enforcement to report undocumented immigrants.

Strong feelings

Survey respondents were first asked to rate how important each issue was to them, and how they would vote in each proposal (in favour, opposed, or abstain).

For storable votes, participants were then granted one extra vote to support a proposition that they felt strongly about. For quadratic voting, respondents were given a choice of extra, weighted votes to express their strength of feeling.

For example, a voter could choose to cast an additional vote on each proposal, each weighted as 1, or to cast only one additional vote on a single issue, but with a weight of 2. These priorities were factored into the final outcome by counting the weighted number of cast votes, rather than the total number of voters, to reach a majority.

Casella and Sanchez used their survey result to simulate two sets of 10,000 elections, one performed under each voting system. They found that there was a one in three chance of at least one proposition being won by a minority of voters 鈥� but surprisingly, that left people happy overall.

By using voter鈥檚 ratings of importance on each issue, the pair were able to calculate the 鈥渨elfare鈥� of the outcome 鈥� how much people were satisfied by the result. 鈥淥n average, these minority victories come with improvements in our measure of welfare, suggesting that the minority tends to win when it holds stronger preferences than the majority, stronger enough to compensate for its smaller size,鈥� says Castella.

鈥淚f this paper鈥檚 conclusions continue to hold up, I think there is a good chance that quadratic voting will become increasingly prevalent for collective decision-making,鈥� says Glen Weyl of Princeton University in New Jersey, one of the originators of quadratic voting. Although it might take a while to be used in public elections, it could find use in corporate decision-making, he says.

Casella also believes quadratic and storable voting could prove useful in the real world. 鈥淚t may be appropriate to start experimenting with them,鈥� she says. But while she believes studying the weaknesses of majority systems is important, she is reluctant to suggest that they be done away with altogether. 鈥淢ajority voting has very strong legitimacy.鈥�