What is the chance of an MP being wrong?
When MPs took a maths exam it showed that the members of parliament are pretty bad at elementary probability. When asked “if you spin a coin twice, what is the probability of getting two heads?” 47% of conservatives and 77% of the Labour MPs gave the wrong answer. About 75% of the MPs felt confident when dealing with numbers, although they generally though politicians did not use official statistics and figures correctly when talking policy.
How should a rational person react to this news?
If your ability to make rational inferences about probabilities and likelihoods is bad, then your decisions will be irrational. Relevant information will not affect your decisions in the way it should, and they will be suboptimal and biased. So insofar politicians are seen as decision-makers this is very, very bad news. Many, if not all, government decisions deal with reasoning under uncertainty and dealing with numerical data. Especially thinking about risk requires nontrivial understanding of probabilities.
Even worse, being a rational decision-maker doesn’t seem to influence your chances of winning a political position. The question about how other politicians use numbers show that the MPs are likely aware of the sloppiness, but their own confidence suggests that they are strongly overconfident in their own limited abilities. It is pretty likely that voters select for confident people rather than people who make the right decisions – or care about their rationality.
However, politicians also have a role as representatives and exponents of preferences of the electorate. In this case the problem might be smaller: we can hope they set the right agendas, and then civil servants who know probability do the proper implementation. Unfortunately there is no reason to assume civil servants are really rational with probability either, and if the policy has been set on irrational grounds – perhaps due to misunderstood figures – then even a rational implementation will be faulty.
A final save might be if it is about framing and ecological validity. Maybe the politicians are bad reasoners about abstract probabilities but do a decent job for real likelihoods. As Leda Cosmides and John Tooby showed in the Wason card task, people are much better at reasoning about a social situation than an equivalent abstract one. So maybe the politicians would not think that a policy requiring project A and B to both succeed has as good chance of succeeding as one dependent on just one of the projects. But I have my doubts.
Having fallible, irrational and biased agents is not necessarily a problem for the collective rationality of a system if care is taken to design it to filter out these factors (consider how the Condorcet jury theorem, rewards tied to correct decisions, or peer review systems can improve things). But if the system is designed by agents that do not care about its rationality (because they do not see the importance, or because they are not rewarded for doing it), then it will likely just distil certain biases. Powerful systems will then promulgate and enforce those biases onto other individuals, even when the individuals would not have made the same decisions if they could have acted freely.
So a rational citizen would likely want to either reduce the power of the irrational government (assuming that decision capacities now would be in the hands of people with individual incentives for being rational; there is no use in reducing government if power over you just moves to other irrational institutions), or lobby as hard as he can to make other voters to put pressure on politicians to construct pro-rational decision-making procedures. Sounds like that goal would need a very catchy slogan to get anywhere.