## Confusing with complications

I’m reading this awesome article by Srinivas Bhogle (with Rajeeva Karandikar) on election forecasting. To be fair, not much of the article is new to me – it’s just a far more readable version of Karandikar’s seminal presentation on the topic made at IIT Kanpur all those years back.

However, as with all good retellings, this story also has some nice tidbits. This one has to do with “index of opposition unity”. The voice here is Bhogle’s:

It is easy to understand why the IOU becomes so critical in such situations. But, and here’s the rub, the exact mathematical formula connecting IOU to the seat count prediction is not easy to find. I searched through the big and small print of The Verdict by Dorab Sopariwala and Prannoy Roy, but the formula remained elusive.

Rajeeva suggests that it was likely based on simple heuristics: something like ‘if the IOU is less than 25%, give the first-placed party 75% of the seats.’ It may also have involved intelligent tweaking based on current survey data, historical data, informal feedback, expert opinion, gut feeling, and so on.

I first came across the IOU in Prannoy Roy and Dorab Sopariwala’s book. The way they had presented in the book, it seemed like it is a “major concept”. It seems, like I did, Bhogle also looked through the book trying to find a precise formula, and failed to do so.

And then Karandikar’s insight above is crucial – that the IOU may not be a precise mathematical formula, but just an intelligent set of heuristics, involving intelligent tweaking.

Sometimes putting a fancy name (or, even better, an acronym) on something can help lend credibility to the concept. For example, IOU is something that has been championed by Roy and Sopariwala for years, and they have done so to a level where it has become a self-fulfilling prophecy, and a respected scientist for Bhogle has gone searching for its formula!

Also, sometimes, telling people that you “used an intelligent heuristic” to come up with a conclusion can lead you to be taken less seriously. Put on a fancy name (even if it is something that you have yourself come up with), and the game changes. You suddenly start to be taken more seriously, like Ganesha assumed when he started sending fan mail under the name “YG Rao”.

And like they say in The Usual Suspects, sometimes the greatest trick that the devil ever pulled was to convince you that he exists. It is the same with “concepts” such as IOU – you THINK they must be sound because they come with a fancy name, when all that they apeear to represent is a set of fancy heuristics.

I must say this is excellent marketing.

## Opinion polling in India and the US

(Relative) old-time readers of this blog might recall that in 2013-14 I wrote a column called “Election Metrics” for Mint, where I used data to analyse elections and everything else related to that. This being the election where Narendra Modi suddenly emerged as a spectacular winner, the hype was high. And I think a lot of people did read my writing during that time.

In any case, somewhere during that time, my editor called me “Nate Silver of India”.

I followed that up with an article on why “there can be no Nate Silver in India” (now they seem to have put it behind a sort of limited paywall). In that, I wrote about the polling systems in India and in the US, and about how India is so behind the US when it comes to opinion polling.

Basically, India has fewer opinion polls. Many more political parties. A far more diverse electorate. Less disclosure when it comes to opinion polls. A parliamentary system. And so on and so forth.

Now, seven years later, as we are close to a US presidential election, I’m not sure the American opinion polls are as great as I made them out to be. Sure, all the above still apply. And when these poll results are put in the hands of a skilled analyst like Nate Silver, it is possible to make high quality forecasts based on that.

However, the reporting of these polls in the mainstream media, based on my limited sampling, is possibly not of much higher quality than what we see in India.

Basically I don’t understand why analysts abroad make such a big deal of “vote share” when what really matters is the “seat share”.

Like in 2016, Hillary Clinton won more votes than Donald Trump, but Trump won the election because he got “more seats” (if you think about it, the US presidential elections is like a first past the post parliamentary election with MASSIVE constituencies (California giving you 55 seats, etc.) ).

And by looking at the news (and social media), it seems like a lot of Americans just didn’t seem to get it. People alleged that Trump “stole the election” (while all he did was optimise based on the rules of the game). They started questioning the rules. They seemingly forgot the rules themselves in the process.

I think this has to do with the way opinion polls are reported in the US. Check out this graphic, for example, versions of which have been floating around on mainstream and social media for a few months now.

This shows voting intention. It shows what proportion of people surveyed have said they will vote for one of the two candidates (this is across polls. The reason this graph looks so “continuous” is that there are so many polls in the US). However, this shows vote share, and that might have nothing to do with seat share.

The problem with a lot (or most) opinion polls in India is that they give seat share predictions without bothering to mention what the vote share prediction is. Most don’t talk about sample sizes. This makes it incredibly hard to trust these polls.

The US polls (and media reports of those) have the opposite problem – they try to forecast vote share without trying to forecast how many “seats” they will translate to. “Biden has an 8 percentage point lead over Trump” says nothing. What I’m looking for is something like “as things stand, Biden is likely to get 20 (+/- 15) more electoral college votes than Trump”. Because electoral college votes is what this election is about. The vote share (or “popular vote”, as they call it in the US (perhaps giving it a bit more legitimacy than it deserves) ), for the purpose of the ultimate result, doesn’t matter.

In the Indian context, I had written this piece on how to convert votes to seats (again paywalled, it seems like). There, I had put some pictures (based on state-wise data from general elections in India before 2014).

What I had found is that in a two-cornered contest, small differences in vote share could make a massive difference in the number of seats won. This is precisely the situation that they have in the US – a two cornered contest. And that means opinion polls predicting vote shares only should be taken with some salt.

## Opinion polls and betting

So for a change the opinion polls seem to have got it right. I’m talking about the just-concluded elections in the UK here, which has returned a hung parliament. The Tories have fallen just sort of a majority (in Kannada we’d call it “AJM“). It’ll be interesting to see how a government will be formed now.

Now, the thing is that the opinion polls got it right. While the Tories had started off with a big lead at the time the elections were announced, opinion polls over time showed that the race was getting a lot tighter. I’d piggybacked on the opinion polls to conduct my own analysis which got published in Mint.

Having shown off that I’d made the prediction correctly, let me get to my hypothesis of why the opinion polls got it right. Opinion polls in the UK have a greater chance of being right because because betting is legal here.

I was walking around Central London yesterday when I saw this poster outside a betting shop.

Because betting is legal in the UK, betting houses take bets on just about anything, including the results of elections. The way betting works is that the betting houses make markets. They present odds for each side of the deal (in this case, let’s say Tory win, Labour win and hung parliament), and whenever a punter walks into the shop and places a bet, it’s the house that’s taking the opposite side of the bet.

What this implies is that the house better get the odds right, otherwise the difference in their odds and the actual results can wipe out the shop. And how does the betting house know where to set the odds? For something like an election, they rely on the opinion polls.

If the opinion polls get it wrong, the betting houses can end up losing a lot of money (like they evidently did last year during the Brexit vote which most pollsters got horribly wrong). So there is a legal entity which has real skin in the game in opinion polls being right.

I’m not sure of the ownership of the opinion polling companies here in the UK, but I won’t be surprised if they make plenty of money by selling their results to betting shops (at a more granular level than what they make public). And given the intense competition among pollsters here in the UK (at least 15 different agencies conducted opinion polls ahead of yesterday’s elections), there is a real incentive for a pollster to get it right – get it wrong and the betting houses might take their business elsewhere.

In case betting wasn’t legal (such as in India), polling agencies wouldn’t be able to legally sell their results to betting houses and punters, and their markets would be limited to media houses. Media houses don’t have that much of a skin in the game in the polls – their profits don’t depend on getting polls right as much as the profits of betting houses. And pollsters would have less incentive to get the polls right.

Now, howzzat?