A question of transitivity: Why predicting electoral outcomes is hazardous

The context for this article is the focus on 2023. Forget everything else; it's going to be the nine assembly elections due next year. These are coming on top of the six in 2022 in which the BJP lost two and has a coalition in one.

But why does a political party which wins in one state lose in another even when elections are held within a few months of each other?

Political pundits give all sorts of reasons in terms of anti-incumbency, choice of candidates, constituency-specific factors like caste, corruption, economic factors etc. These are all correct, no doubt. But even when we add them all up, we don't get a complete explanation, for which we have to look elsewhere.  

That "elsewhere" is the breakdown of transitivity in some circumstances. Transitivity is about how preferences are ordered. Thus, if you prefer a prawn curry over a mutton curry which you prefer over a vegetable curry, then you must also prefer the prawn curry over the vegetable curry regardless of where you are.

But this is not always the case. There can be circumstances when the vegetable curry is preferred to both the prawn and the mutton curry. This happens when transitivity breaks down and we get an intransitive preference ordering, leading to logically inconsistent outcomes.

For example, why do people in adjacent constituencies vote for different parties even when the two constituencies are small, as they were in Himachal? If the BJP is definitely preferred to the Congress, which is preferred to other parties, then the BJP must be preferred to all other parties, right, in all adjacent constituencies? Well, no.

As we saw in Himachal, the Congress was preferred to the BJP. But in Gujarat, it was the opposite. BJP was preferred to the Congress, which was preferred to the AAP. In Punjab, however, it was a different story. There the AAP was preferred to the Congress and the BJP.

This is a clear case where A preferred to B preferred to C doesn't mean that A is also preferred to C. The transitivity rule has broken down. While in logic, there are clear reasons why this happens, the breakdown is harder to explain in politics and elections.

After all, economic factors and corruption are the same all over India. Political parties also make sure they choose candidates from the same castes. But in the Delhi municipal election, people voted for Arvind Kejriwal regardless of who the candidate was. In Himachal, however, despite the prime minister's exhortation to ignore the candidates and vote for him personally, the BJP lost. That leaves anti-incumbency, but while it was there in Himachal and Punjab, it wasn't there in Gujarat.

What if we add up all these things? Would that explain the absence of transitive preferences? Unfortunately, no. The sum of all prejudices or preferences in one constituency or state doesn't get transferred out of it consistently. Transitivity has broken down. This is a great mystery that no one has been able to explain.

No one has figured out the persistent inconsistencies in voter behaviour. Thus, people can vote decisively against a party and a few years later vote it back just as decisively.

So we are left with just one conclusion: voter behaviour is as unpredictable as the crow on a tree. You don't know in which direction it will fly off. This will be confirmed again in 2023. The BJP has its task cut out.

We have forgotten, but in 2014, just six months after winning all Lok Sabha seats in Delhi, the BJP won just two seats in the Delhi state election.