In my last post on Condercet’s Jury Theorem, I showed that by adding two incompetent people into the mix I decreased the group’s chance of voting for the right outcome.
In a large group, an increase in incompetent voters would not be surprising. This was noted by Condorcet himself when he said:
A large assembly cannot be composed of enlightened men; it is likely that its members will be carried by ignorance and prejudices
The presence of ignorant voters suggest that they will make the wrong decision (assuming we’re still considering questions that have a right/wrong answer). The reason why they’re ignorant could be explained by Downs’ rational ignorance hypothesis. Downs concluded that since each voter has a negligible chance of affecting the outcome, they will have little incentive to inform and educate themselves to make the right decision. In other words, they make a rational decision to be ignorant.
If every individual adopts this reasoning then all voters would be ignorant, and democracies would fail at making informed decisions. Yet a paper by Martinelli in 2006 posited that in certain circumstances, rational ignorance can still be consistent with the majority making an informed decision.1
This old article from New Republic discusses the phenomenon. A survey of Americans revealed that more than half could not name any Supreme Court Justice. Yet, while only 12 per cent could name Ruth Bader Ginsburg as a Justice, 71 per cent were able to offer some opinion of her (36 per cent favourable, 35 percent unfavourable).
Perhaps they were rating justices randomly, yet the survey results also showed that in the end 56 per cent of liberals offered a favourable view of Ginsburg, while only 25 per cent of conservatives did. Are these the results we would expect from purely random ratings? The article concludes:
people seem able to make pretty good use of the limited political knowledge they do have…And, keep in mind, that’s all it takes for democracy to work. As long as the votes of genuinely clueless citizens aren’t systematically biased in any ideological direction (and, by definition, they’re unlikely to be), once votes are aggregated, the results are apt to reflect the real preferences of the populace.
Martinelli also echoes this in his paper when he says:
…our results support the idea that elections serve the interests of the majority better than what the rational ignorance hypothesis would seek to indicate at first glance…They suggest that models of public opinion that take into account the production of information by the media, interest groups, and the like, can be enriched by considering the aggregate implications of voters investing somes small (but positive) effort in costly information processing.
In other words, a rationally ignorant society can still vote and make informed decisions. While the cost of processing information remains high, in a world where information (either from the media, or lobby groups) is readily available, voters only need to put in a small amount of effort (i.e. pay a little attention) to gain the edge.
- Martinelli uses a lot of maths to prove this which I won’t go into here. Roughly speaking, it involves finding an equilibrium where it is optimal for every individual to invest some tiny, but positive, effort into acquiring information.