# Betting on opinion polls

You may have heard of PredictIt, the political futures market. It allows users to make and take bets on a wide variety of political outcomes. Several markets ask you to predict the presidential job approval ratings at a future date. The site typically relies on a poll aggregator such as FiveThirtyEight or (more commonly) RealClearPolitics. You can bet anywhere from 1 to 99 cents on the outcome falling inside or outside a certain range, and you win a dollar if you’re right.

Actually, you don’t have to bet on the most likely outcome to make money in the long term. You only have to find people offering bets with the wrong odds. For example, say I’m offered the following game: Pay 1 cent to play, then shuffle a deck of cards and pick one. If it’s the ace of spades, I win a dollar. I can play as many times as I want. Even though I expect to lose on a given round, in the long run I’ll profit because it only takes me about 52 cents to win a dollar. In other words, the game is underpriced relative to its odds.

Thus, the way to play the game is not to predict the most likely outcome, but rather to calculate the probabilities of all outcomes. Start with historical data scraped from RealClearPolitics, for about a year ending in February 13, 2018.

We can look at the distribution of daily changes, which looks normally distributed. Here I’ve plotted a normal fit over the histogram of steps.

Actually, a random walk with normally distributed steps (also called a “Gaussian random walk”) has some nice properties. If the steps are independently sampled from $N(\mu,\sigma^2)$, then the total change T steps later is sampled from $N(\mu T,\sigma^2\ T).$ That is, it’s the variance which grows linearly with time, not the standard deviation. The mean also grows linearly, as you might expect for a drift process. (Here we assume Markovian behavior; that is, that the system has no memory other than its current state.) Armed with this knowledge, we can plot a distribution on outcomes a fixed time later, say 100 days.

If you’ve made it this far, you’re probably wondering whether each step is really sampled independently from the rest. To test this assumption, we should calculate the autocorrelation function,
$\mathrm{Exp}\Big[\Delta(t)\Delta(t+\tau)\Big]$
as a function of τ, where &\Delta; is a daily change in approval rating.

It drops an order of magnitude between τ = 0 and τ = 1, and stays there. What this tells us is that the underlying system has little memory other than its current value. In fact, this defines the Markov assumption.

Finally, the question is how to place your bet. On PredictIt, the outcomes are binned, so we should integrate the normal distribution over each bin width to get probabilities. From there we can choose the event with the most favorable odds, and use the Kelly strategy to decide how much to bet.

In a later post, I should use historical data to examine the performance of this approach.

# Acting

James P. Van Dyke, with a minor in Psych
wanted to be an actor.
He dreamed every night of his name up in lights
and audience roaring with laughter.
So he moved to L.A. and got started that day
scrubbing dishes and floors at a diner.
And ignoring the fact that his acting was crap,
his scrubbing could not have been finer.

James P. Van Dyke, with a minor in Psych
waited from Winter to Fall.
But no agent, he found, after looking around,
would return even one of his calls.
Having sought wealth and fame he had reaped only pain,
his dream all but withered and gone.
Not food, love, or drink, nor the couch of a shrink
could give him the will to go on.

James P. Van Dyke, with a minor in Psych
to talk to no other but dear loving mother
and try not to put up a fight.
“James,” she would say, in her matronly way,
“You’re a failure who’s run out of luck.
No one will hire a talentless liar.
You’re not an actor—give up!”

James P. Van Dyke, with a minor in Psych
would be dead with a shell in his brain
were it not for a pill to resolve any ill-
ness in sunshine, in fog, or in rain.
An antidepressant for gods and for peasants,
for children and wombats and bears.
It’s easy to throw back your woes with a Prozac
and live without worries or cares.

James P. Van Dyke, with a minor in Psych
got a phone call from Pfizer one day:
“We wondered if you would be willing to do
a testimonial sometime in May.”
So he went to rehearsal for the Prozac commercial,
which aired on T.V. soon thereafter.
But his face turned pale green when it said on the screen,
“James is not an actor.”

# A joke which requires lack of knowledge to understand

Usually “getting” a joke requires some subject knowledge. For example, you have to know who Michael Jackson is in order to understand Michael Jackson jokes. I came up with a joke which requires partial knowledge as well as partial ignorance. The joke is:

What emoji is missing on Chinese phones?