A Skeptical Audience

So Donald Trump fired FBI director James Comey, as everybody knows by now. This immediately drew parallels to the Saturday Night Massacre, where Nixon ordered his Attorney General to fire special prosecutor Archibald Cox.

At the heart of the matter are three questions. First, whether Comey was the best person for the job. The second question is whether this will hinder any ongoing investigations, specifically the investigation into Russian involvement in the Presidential election; and what if anything will be done to safeguard these investigations.

The third question is the most important, and is simply; which of the first two questions did Trump answer when firing Comey? That is, did he fire Comey because he felt Comey wasn’t a good director? Or did he fire Comey specifically to stop the Russian investigation (or any other)?

If it’s the first, and Comey wasn’t the best fit for the job (or even if Trump just honestly thinks so), then there’s no real problem. If it’s the second, then basically Trump is abusing the office to enact a personal agenda, using the department of justice as a political tool, and obstructing justice. Essentially, what Trump did is either a standard (if somewhat unusual) way of acting as President, or an impeachable offense; either it was as bland as Bill Clinton dismissing FBI director William Sessions, or as corrupt as Nixon firing Cox.

* * *

Having just finished a class on negotiation; I was struck by an study by Huthwaite inc, called “The Behaviors of Successful Negotiators” which looked at (no surprise here) the behaviors of successful negotiators. It was one of those truly great readings, the point of which seems obvious to me after reading it, but never once occurred to me beforehand. There were some behaviors which were kind of boring, (such as skilled negotiators talking more about long term topics), some which were somewhat reasonable but not much use elsewhere (skilled negotiators don’t have a predetermined sequence of when they wish to discuss which issue), but some which were meaningful and profound.

The fact I was most impressed with were the fact that skilled negotiators rarely used words like “generous,” “fair,” or “reasonable” to describe their own offers. Within a negotiation, calling something “fair” which you present, even if you think it is fair, is unlikely to convince your counterparty; it will only serve to aggrevate him or her if they don’t think its fair.

The second fact which I thought was really valuable was that skilled negotiators often made fewer arguments in their favor; but those were typically better quality. That is, if you’re trying to convince a hostile (or even skeptical) audience of a fact, and you present 5 arguments, they’re naturally going to latch on to the weakest argument you make. People are not rational Bayesian calculation machines, 2 strong arguments in favor are greater at convincing humans than 3 strong and 3 weak arguments in favor.

In both cases, the lesson is similar, in convincing a skeptical audience less is often more. Using more neutral language is more persuasive than persuasive language, and using fewer arguments is more persuasive than using many. The stronger you believe something (or come across as believing that thing), the less persuasive you can be to a skeptical audience.

* * *

Today, while packing up my apartment, I was listening to a several months old episode  of Bill Simmons’ podcast, the BS report. Simmons’ guest was one of my favorite essayists, Chuck Klosterman. In it, they were discussing who the NBA MVP will be, Russell Westbrook or James Harden. Klosterman had a very intriguing argument, which essentially went like this (I am of course paraphrasing):

1: The people who favor Westbrook think its obvious that the MVP should be Westbrook and there’s no other choice. (Westbrook averaged a triple double over the season, something that hasn’t been done since the legendary Oscar Robinson).

2: The people who favor Harden think its an interesting question and there are arguments for multiple candidates, but Harden is overall their favorite.

3: The people who are undecided will see the above two arguments, and almost tautologically will relate to 2nd one more. Because (by definition) they haven’t made up their mind, they can relate to those who think its a close race, who favor Harden.

Its an almost brilliant idea, and I have no idea if it will be correct or not, but it has a certain logic to it. Underlying it all is the same lesson, your ability to convince a skeptical party of something can be inversely related to the strength of your own belief.

* * *

Trump’s approval rating is low, but its not historically low. 538.com has him at 41%; Gallup had Obama at the low 40’s for much of 2011 and 2014 (of course this time in 2009 Obama was in the low 60’s, 20 points better than Trump is now.) Gallup had W Bush’s low at 25%, HW Bush at 30%, Clinton at 40%, Reagan at the mid 30’s, Carter at 30%, and Ford at 40%. (the counterclaim is that none of these Presidents were this unpopular this soon in their Presidency, but that’s kind of beside the point).

I’m not a Trump fan, and I certainly don’t think I will be. I see a number of things which Trump has done as being bad, corrupt, or incompetent, and the demeanor in which he has conducted himself has at times seemed unhinged and almost crazy. This to go with his numerous scandals, problems, gaffes, and remarks he made while campaigning and as a public figure.

Yet as much as 41% of American voters still approve of Trump. Why is this?

* * *

All this brings us back to President Trump and James Comey. If you’re already inclined to believe that Trump is a despot you will probably see the Comey situation as analogous to the Saturday Night Massacre, and Trump as obstructing justice. If you’re a fan of Trump you’re much more likely to see the situation as nuanced, or as analogous to Bill Clinton dismissing Director Sessions. And if you’re in between? Well, articles like this probably won’t convince you.

I think that those people who either support Trump or at least still giving him the benefit of the doubt just see all the criticism blending together, drowning itself out. They see Trump detractors reacting to firing Comey in the same way the reacted to Trump’s February 16 press conference. As long as they see the tone and not the substance of their opponents’ arguments, they’ll get no new information, and of course won’t change their minds.

Take an article like this, very anti-Trump, which purports to list all the bad things Trump has done. Yet it seems like half the things listed aren’t things Trump has done, but rather things he’s said or tweeted. Going back to the fact about skilled negotiators, how they will use fewer stronger arguments. Then compare that to the list in the nymag article. For many of the “Trump said this” arguments, if you’re not convinced now, you may not be ever. And if that argument won’t convince a skeptic, then making it will probably make better arguments less convincing.

With a skeptical audience, the strength of your beliefs can often work against you. There’s no shortage of liberal antipathy towards the Trump administration, yet I wonder if the strength of the left’s beliefs is actually hindering its ability to make a convincing argument.

Playing the lottery is not a Sharpe choice

The Powerball Jackpot is approaching $500 million dollars tonight.  The chances of winning are 1 in 175 million. Which gives the expected value of $2.86 per ticket, and at a cost of $2 per ticket, that’s a great value!

Of course, the 500 million is an annuity, the “lump sum” or the real value is 337, which gives a value of $1.92 per ticket. This is increased by all the other prizes, as one can win $4, $7, $100, $10,000 and $1,000,000 for various combinations. Doing the math (which I won’t spell out in this post) gives you about $0.36 per ticket, so for tonight’s jackpot we can estimate the expected value of a single ticket at $2.28, or roughly a 10% average return.

If, as we’ve calculated, the expected value of the ticket is $2.28, is buying a ticket the economically intelligent thing to do? What, for that matter, does expected value actually mean?

One way to think of it is to imagine buying all possible tickets. There are 175 million possible number combinations (thus the 1 in 175 million chances), if you bought every possible ticket, you would be guaranteed a winner, (and multiples of all the lesser prizes) which means that buying all the tickets will make you money, about $400 million to be approximate. If buying all the tickets will get you x amount of money, then buying 1 ticket will get you x/175 million in money; doing this math gets us to the $2.28 figure.

But there’s something else to consider, that is the possibility of another winner. If two people win the prize, then the prize amount drops in half. Lets say, for the sake of simplicity, that there is a 40% chance of having two winners (which, if anything seems too low, it seems like when lotteries get this high). That reduces the expected value of the ticket from 2.28 to 1.90, which makes it fall below our magical $2 level.

But what is this telling us? Well, it tells us that if we buy all the tickets, now we will expect to lose money. But why does this have any relevance for anyone who buys a single ticket? Lets imagine a scenario. First, lets assume that, for whatever reason, the jackpot is rarely split in two so you barely figure that into your calculations (maybe a 1% chance of two winners instead of a 40% chance). Now, imagine that you buy a Powerball ticket, and to your joy while watching the drawing you see each of your 6 numbers match those being drawn. As you’ve just one the jackpot, you are ecstatic. The next day, as you get the morning newspaper, you see the headline: “Record Powerball Jackpot has 2 winners” Instead of winning the full jackpot, you only win half. Now, do you regret buying the ticket? Of course not, ex ante, the math worked in your favor, ex post, the math worked in your favor.  So why, if when event x happens it does not cause you to change any rewards scheme, should the possibility of event x enter into your calculations?   No realistic number of winners will ever push the jackpot down to a level where you wouldn’t be happy winning it.

Lets change gears a moment and talk about taxes. Assume that taxes takes away half the winnings.  Business Insider did the math here: basically the taxes push the expected value to $1.32 (for some insane reason they are reporting the expected return on buying a ticket, instead of the expected value of a ticket.) They figure that you should apply the after tax return to the cost of buying a ticket to determine the expected value.

But what does our analysis actually mean? If we return to the scenario of buying every ticket, all in all we’d spend about $350 million, get the jackpot and all the other prizes, for a value of about $400 million. Now, if you assume that you would pay half that $400 million in taxes, you’d be left with $200 million, or a loss of $150 million, so you figure don’t buy the tickets. But in reality you wouldn’t be charged $200 million in taxes, because of the ability to write off gambling losses against gambling wins. So instead of paying $200 million, you would only pay $25 million in taxes (on 50 million net winnings), which pushes the net value to positive territory.  So which value is correct? One the one hand, you’re not actually buying all the tickets, and the value of a single ticket as a tax write off is negligible. On the other hand, it’s not like paying the taxes on the winnings is going to make a big difference, you’ll still be horribly rich. So what is the answer?

The answer is that there is no answer. Using something like expected value is a tool which helps us understand our world, but it is not the world. For any Powerball lottery, there is always a very small chance that you will become very rich. Exactly how rich is hardly an interesting question. Imagine yourself with $100 million. Now imagine yourself with $200 million. There isn’t much of a difference. Or to put it differently, think of all the things that you could do with $200 million that you couldn’t do with $100 million: not a gigantic difference. So if the human difference between 100 and 200 million dollars isn’t big, what is the point in taking the jackpot, multiplying it by the probability of winning, and comparing that number to the ticket price? If you win, you’ll be happy. If you lose, you wasted money. In other games with lower variance in returns (such as roulette) can help you understand whether you will win or lose over the long run, in the case of roulette the long run is over an hour or a few hours. But in Powerball, the long run would last millions of years (potentially billions if you only play when the Powerball odds are in your favor), so how is that useful?

In finance, there is a concept called the Sharpe ratio. It measures the marginal change in return to marginal change in risk. Basically, it’s a way of adjusting returns for risk. If I did my math right, in our situation we an expected return of about .14 (winning 2.28 on a 2 dollar ticket is a 14% return, we can assume the risk free rate of return is zero overnight (close enough anyway), and a standard deviation on the return of 162 million. Which gives us a Sharpe ratio of 0.00001123293428; well below the advised value of 1 for a decent risk adjusted investment. It’s not perfect resolution of the problem, but it does illuminate the basic problem with Powerball, if it’s worth $2 for a 1 in a 175 million chance to win $300 million, it’s probably still worth $2 for a 1 in a 175 million chance to win $40 million, big changes in very low probability events just aren’t significant.