Long live the majority!

This post was first published in 2006 on the Alphapsy blog.

"How should groups make decisions?" this old question is on the way of being answered, as researchers Reid Hastie and Tatsuya Kameda vindicate the use of the majority rule. In a paper published last year in Psychological Review, the authors show by means of extensive simulation and experiments that in a wide range of cases choosing the answer that is favored by most people in the group is the best way to go.

Ever since Condorcet (actually, his name is Marie Jean Antoine Nicolas Caritat, marquis de Condorcet, allowing him to compete for the ridiculously long name award) started using mathematics to try to prove the efficiency of democratic rules, economists and political scientists have struggled to try to determine what is the optimal way for groups to make decisions.

Hastie and Kameda give interesting evidence for what they dubbed the "Robust Beauty of Majority Rules". The simplest and most well known majority rule is actually a rule with weaker contrainsts than the pure Condorcet majority rule: it is the plurality rule. This rule is quite straightforward: the opinion that is supported by the most people wins.



The researchers pitted this rule against a range of other rules, some well known (averaging) and some more obscure (the Borda rank winner). In the first test, they devised a simulation in which several agents had to guess which of ten virtual patches of resources would be the best, using imperfect cues about the amount of resources present in each patch. The choices of the agents was then aggregated following the different rules, and the efficiency of the result (would the aggregate point to the best patch) was calculated for a large number of rounds.



Over a wide range of parameters, it was observed that the most efficient rules were averaging and the plurality rule. Most interestingly, these strategies regularly beat another rule that has its own intuitive appeal: the best member rule. When this rule is followed, the choice of the member that has the best record of finding the correct patch is followed, and the choices of the other members are not taken into account.

As the authors point out, averaging is a much more demanding strategy (in terms of resources) than the plurality rule. Imagine that a group has to decide on ten canditates. On the one hand, for the averaging strategy to be effective, each member has to give an estimate of each candidate, and these estimates are then averaged. On the other hand, the plurality rule only asks of each member to choose her favorite candidate, and the candidate with the most votes wins. So this strategy is simpler both for the participants and for the aggregation process. Since the plurality rule and averaging tend to yield similar results, the former can be considered the winner of the simulation.

The authors then tested the robustness of this result by using real agents (psychology students) instead of virtual agents. The task was otherwise similar (determination of a best choice among finite options with reliance on imperfect cues). And the results were also similar. They leant even more towards the plurality rule since in no condition was it beaten by the best member rule. This very simple majority rule seems to be surprisingly effective.

I would like to end with two caveats though. First, the authors are speaking of 'group' decision-making. However, no group discussion was involved: the results of the member of the 'group' were simply aggregated. This is a fair assumption since the results of many group experiments can be modelled by a majority rule. However in some cases a different pattern is observed. This is for example the case when the group is confronted to a problem that has a relatively simple normative answer, such as mathematical or logical problems. Then, the result of the group discussion is usually called 'truth wins': as long as one member of the group has the correct answer, and is able to justify it appropriately, then the others end up accepting her solution, even if there was a majority of wrong answers before the group discussion. So this is a case were an actual group process can lead to a better result than the plurality rule. (I should also point out that group discussion can also amplify certain biases, rendering the group discussion less efficient than the plurality rule in these cases).

The second concern is linked to the fact that the participants (or even more the virtual agents) were all equally expert in the task. It is obvious that in more (if not most) real-life group-decision-making contexts, the expertise of the participants will be more variable. If this is the case, then the best member rule could prove to be efficient. However, the group then has to find a good way to evaluate the expertise of its different member and this process might undermine the efficiency of the best member rule to the point that it might be beaten by the majority rule (who also has the advantage of being the less effortful).

Lastly, I recommend this very nice book that defend the crowds (and their majority rule effects) against the slander that often targets them.

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