I still wouldn't play the lottery

Having a lot of math friends, I heard a few of them bought lottery tickets last week, when the expected value of the ticket was greater than the price.  Shit math people say, amirite?

The positive expected value is due to the record-breaking size of the jackpot.  It was $640 million if chosen to be received over 26 years, or $462 million if received all at once.  It's less than that when you subtract tax, but it's still enough to overcome the $1 ticket price and 1/175M probability of winning the jackpot.  (There are smaller prizes, but they have negligible expected value.)

My understanding is that a small percentage of ticket sales goes to the jackpot.  So the record-breaking jackpot is the result of a lot of people spending money on tickets when there was a negative expected outcome, and winning even less money than is statistically expected.

The positive expected value of lottery tickets is greatly mitigated by the fact that if multiple people win the jackpot, they split it amongst themselves.  I am not sure how many people bought tickets, but according to CBS news, ticket sales that week were projected to be $1.46 billion.  With those numbers, you'd expect a lot of simultaneous winners.  There were only three.

But even ignoring the probability of splitting the jackpot, I still don't think it is a good idea to play the lottery.  Why?  $462 million is not 462 million times more useful than $1.

Put another way, imagine that 462 million people all gave a dollar to one person.  That person is rich, rich, rich, on account of having received money from a lot of people.  Wait, why are we all paying this rich person? If we're going to give away money, isn't it better to give it to the poor, and equalize wealth?

Put another way, if I start increasing the amount of money I have, starting from zero, what will I spend that money on?  At first I'd buy food.  Then I'd rent an apartment.  Eventually I'd have enough to get a car.  Much later, I could afford a house.  Later I could afford to retire early, or hire servants (or whatever rich people do with their money).  The point is that the money I get early on is used to buy essential goods, while later money is used to buy luxuries.  I could choose to buy luxuries even when I'm poor, but I'd much rather buy the essentials, because that's more for my money's worth.  The result is that a dollar is more useful to a poor person than a rich person.

One way to capture this intuitive idea is with a utility function.  (Insert standard disclaimer about not having any economics education.)  A utility function is just a way to express how preferable something is.  So if we're considering money, U($x) tells you the utility of having x dollars. The greater the utility, the more preferable it is.

If we assign a numerical value to utility, we can speak of the expected utility of buying a lottery ticket.  Suppose we start with $10000.  Then the expected utility of buying a lottery ticket is approximately as follows (ignoring tax):

U($9999) * (1 - 1/175M) + U($462M) * (1/175M)

And of course, this needs to be compared with the utility of not buying a lottery ticket, which is U($10000).

Common sense says that U($10000) is greater than U($9999).  But common sense also says that U($x) increases more slowly as x becomes greater (ie U is concave), because the more money you have, the less useful each dollar is.  One possible function which fits these criteria is U($x) = Log(x).  This is not the only possible utility function, though in some sense it is the "correct" one, for reasons I don't at all understand.  Using this utility function, here's the expected utility:

Expected utility of not buying a ticket: U($10000) = 4
Expected utility of buying a ticket: U($9999) * (1 - 1/175M) + U($462M) * (1/175M) = 3.9999566
Expected utility of dropping a dollar in a hole: U($9999) = 3.9999566

So yeah...

Buying more tickets is actually worse, because the difference between U($9999) and U($9998) is greater than the difference between U($10000) and U($9999).  I estimate you'd need about $100M before it becomes worthwhile to buy a single ticket.

Of course, as long as we're talking about utility rather than hard money, you could argue that there is utility in being entertained by the lottery.

I leave analysis of Pascal's Wager as an exercise to the reader.

(via Uncertain Principles)

A dilemma on asexuality and race

I am asexual, and I am half-Chinese, half-White.  I don't usually think of these two things as interacting, at least not in my life.  And yet, there I was, having an honest to gods dilemma involving asexuality and race.

I present this workshop on asexuality for queer audiences.  Last year, I presented at the Queer and Asian Conference.  It was successful, and I got the usual positive feedback.  But I had some misgivings.  I felt that what I had to say didn't really have much relevance to the intersection of queer and API (Asian/Pacific Islander) identities.  I make a point to know just a little about every intersection between asexuality and other identities and groups, because that's the sort of knowledge that is handy in a Q&A session.  But could I really say more than one or two lines about it?

I was also worried that it was a relatively small conference, and I was taking too large a slice of the attention pie.  Learning about asexuality does not prevent people from fighting for other causes, but attending this particular workshop would have the concrete effect of preventing people from attending other workshops held simultaneously.

The conference organizers asked me if I wanted to present again this year.  I wasn't sure, so I let the proposal deadline go by.  And then I immediately regretted it.

I had a realization.  I was so worried about "invading spaces", worried about taking up attention with things that are irrelevant to API people, that I ignored what API people were actually saying.  The organizers went out of their way to invite me, and people in the audience thanked me.  And here I was, thinking I knew better than them what they wanted.

It reminds me of something Natalie Reed said in Thoughts from a Diversity Hire.  Some people were saying that including a person from group X is "tokenizing" and "patronizing".  Natalie responds:

This one is especially infuriating in that presuming to speak for us about what would or wouldn’t be patronizing to us is itself patronizing in the extreme.

So that's what I was doing.  I was making assumptions about what API people want, in contradiction with what they said they wanted.  I was part of the problem.

For the record, I know that API people are not monolithic, and some might have the opinion that my workshop was inappropriate for the conference.  I want to hear from these people, if they are out there.  I am willing to listen.

I also realized I was getting a few other things completely wrong.  Such as, where am I getting this idea that the conference needs to be entirely about issues unique to API people?  I know very well that API people share experiences with white people, and are concerned about some of the same topics. Part of the purpose is just about having a social environment with many API people, and if there are any issues unique to us, we'll naturally talk about them along with the other topics.

And where am I getting this idea that there is little intersection between asexuality and race?  I know very well this is not true, but it seemed to have slipped my mind.  If asexuals are uniformly distributed in the population, asexuality is just as much an Asian issue as it is a White issue.  And yet, the publicly visible asexuals are disproportionately white.  An asexual who was Asian asked me the other day if there were any non-white asexuals I knew of, and was clearly disappointed when I could only think of a few.  This is both indicative of, and a contributor to greater asexual invisibility within API and other non-white groups.

And here I am, contributing to the problem even further.  I decided it was less worthwhile to present asexuality to an API audience than to a "general" (but probably predominantly White) audience.  I was further tipping the already imbalanced scales.  If all asexual activists did the same, it would become a major problem a decade down the road.

I was feeling pretty bad about this.  I was trying to come up with new reasons not to present, to justify the actions I already made.  "Presenting takes work, and I want to relax a bit."  "It would be best to present every other year."  "The organizers may want me to fill their workshop schedule, but the attendees are tired of it." Even though these reasons clearly weren't the original reasons why I did what I did.

So I solved the problem.  The workshop proposal deadline passed, so what?  I submitted a proposal the morning after the deadline.  I am presenting at the Queer and Asian Conference again this year.

tl;dr This is an announcement: I will be speaking at the Queer and Asian Conference at UC Berkeley, which is on April 27-29.  Registration is completely free and open.