Ask an Economist (Post #1005 and counting)

[Mise]

Yes, we have rollovers. But your math is wrong.

I didn't post any maths.

First, you have to buy a ticket every drawing, so every drawing is an independent event.

I have no idea what you think you mean by this.

Most lotteries have odds of about, generically, 1 in 200 million.

The UK lottery is a 1 in 14 million of having the correct numbers. Obviously, this isn't the probability that you'll walk away with the jackpot.

So yes, when the prize is 210 million, its economically rational in that your expected payout is greater than your cost.

No it's not. Your expected payout is not greater than your cost.

But wait, you're also not factoring in the likelihood that you share the winning lottery number with someone else, which becomes more likely the more folks in the game and even moreso if you play with numbers < 31 (birthdays people...)

This is all factored into the concept of "expected return". You know what Expectation Value means, right?

In short, it is the rarest of the rare lotteries that is economically rational. I know of 2 in the last 8 years.

Then we're in agreement...

EDIT: Ooh! 1000th post!

 

[JerichoHill]

@@Mise
I *am* an economist... you know...

You posted logic, which is math.

The UK lottery is a 1 in 14 million of having the correct numbers. Obviously, this isn't the probability that you'll walk away with the jackpot.
If you have the right number then you win, unless you split the jackpot.

No it's not. Your expected payout is not greater than your cost.This is all factored into the concept of "expected return". You know what Expectation Value means, right?
No I don't. They don't teach that when one goes through school to be an economist. Never. Nope. Game Theory skips right over that one.

EG:

Cost of a Lottery Ticket = 1 Dollar
Odds of Winning Lottery = a
Odds of Splitting Lottery Prize = b
Taxes = c
Jackpot = x
Discounted Value of Jackpot (most lotteries payout over 20 years) =d

Expected Value

Win ={ [A*P(B|A)] * (X * d)} / (C *d)
Lose = (1-A) essentially 1

EV = Win - Lose
If positive, rational to play.

When you take taxes, and discount the lottery winnings over time, at least in America, the prize needs to hit around 400 million to have a chance to be economically rational. Note that B is however, a non-linear geometric function that increases as X increases.





Then we're in agreement...

EDIT: Ooh! 1000th post![/QUOTE]

 

[Mise]

So... what part of my post do you think was wrong again?

EDIT: Actually, I've noticed something wrong with your calcs, but it might just be nitpicking. Bear with me...

 

[Mise]

Expected Value

Win ={ [A*P(B|A)] * (X * d)} / (C *d)
Lose = (1-A) essentially 1

EV = Win - Lose
If positive, rational to play.

A few things wrong here.

The Expectation value, strictly speaking, is what I believe you were trying to calculate as "Win" above. The Expectation Value answers the question, "if I put in a pound, what would I expect to get back?" You can't get a negative expectation value from this. (Actually, it can be negative, depending on how you formulate the problem, but the differences are trivial.)

Win - Lose is a meaningless number, unless Lose is exactly 1. If Win - 1 is positive, it's rational to play (this would be such a formulation in which the Expectation value can be negative). If Win > 1, it's rational to play (this would be such a formulation in which the Expectation cannot be negative).

In your calculation for Win, the d's cancel. (Unless the curly brackets "{" mean something different to you than they do to me.)

That being said, you are certainly on the right track; I see nothing that, with a few corrections, contradicts my post.

 

[JerichoHill]

So... what part of my post do you think was wrong again?

EDIT: Actually, I've noticed something wrong with your calcs, but it might just be nitpicking. Bear with me...

I kinda did it on the fly as a program compiled.

 

[JerichoHill]

A few things wrong here.



Win - Lose is a meaningless number, unless Lose is exactly 1. If Win - 1 is positive, it's rational to play (this would be such a formulation in which the Expectation value can be negative). If Win > 1, it's rational to play (this would be such a formulation in which the Expectation cannot be negative).
.

See, we're in disagreement on this here, and its likely due to confusing maths.

Given my cost (1) it is rational for me to play if my Expected Value is greater than 1, neutral if 1, and irrational if less than 1.

I however, did not include a variable (psychic benefit) which should also be included. To further complicate the model, we would need to know how people value the dollar they would spend on the next best alternative, because at various incomes, an extra dollar has differing utilities, and we'd need to check the expected utility from the next best alternative as well. It will get rather messy math wise, but I assure you, I know my probability theory.

In the end, the odds that it is an economically rational play approximates an asymtopically approach to 1 (neutral) as the prize gets larger.

 

[Mise]

I'm glad we've got passed the boring maths part (that's why I didn't bother putting any numbers in - I felt it was enough to say that it was possible that the expectation value could be greater than 1 with sufficiently high jackpots/rollovers.)

Surely, though, anyone who plays the lottery necessarily holds the act of playing the lottery with sufficiently high value that the utility of playing is greater than the cost?

 

[JerichoHill]

Surely, though, anyone who plays the lottery necessarily holds the act of playing the lottery with sufficiently high value that the utility of playing is greater than the cost?

The research suggests that hardly anyone puts that much thought into it.

 

[Bigfoot3814]

Is that the WuTang Financial logo in your avatar?

 

[JerichoHill]

Diversify your portfolio beaches!

 

[Bigfoot3814]

Invest in some nuclear bombs. Send my regards to Ol' Dirty. Dudda dudda dudda.

 

[Mowque]

on a scale of 1-10, ten being absolutely nuts...how crazy is it to want to go back to the gold standard? (A friend was talking about it, and it went a little over my head)

 

[JerichoHill]

around a 9. Every nation is off the gold standard. You'd have to reconvert most of the world.

 

[Panopticon]

There are so many economics articles in journals on lottery behavior that would refute your statement. Further, that we talk about the lottery as a rational expectations game IMPLIES the chance that odds and payout yields an expected value greater than 1 (aka positive return), so your position is incorrect.

If you can, go to your local university library and look up articles in the Journal of Economic Psychology.

I don't have academic access on my present internet connection. A quick search of JEP abstracts returns very few articles about large-scale commercial lotteries, though there are several articles about gambling in a more academic context. Nothing I have read contradicts the theory that people who play the lotto do not believe it is a positive NPV investment in purely cash flow terms - which is the point I was making above. As a good social scientist though I will yield to convincing evidence to the contrary...

 

[JerichoHill]

I'd *love* to be able to give you some of the articles from the journals I can access, but my subscription is for online only and I'm not allowed to distribute copies, especially since they're paid for by the government, who tends to frown on copyright violations.

From what I recall (forgive me, two years ago I was working on a project involving payday loan business, and one of my control variables for demographic purposes had to do with the presence of lottery sales in the area, so that's where I'm remembering alot of this from) For certain subsets of the population, false beliefs about mathematical odds were prevalent (this variable essentially helped explain part of a "discriminatory add-on) to payday loan terms. Generally speaking, this effect was most prominent in large cities with a poor, black, aging, urban core. Think Chicago, Atlanta.

 

[ArneHD]

Two questions: What is the relationship between Psychology/Sociology and Economics and what, fundamentally, IS economics?

 

[JerichoHill]

First, the easier question. Economics is the application of statistical analysis to understand how people choose to use resources.

Resources, being a very loosely defined word.

Psychology attempts to understand the questions surrounding individual behavior, intra-behavior. Sociology attempts to understand cultures. Neither utilizes statistical inquiry to the depth and breadth that economics will do. Yes, they're related, but not in how they ask, and ultimately answer, questions of our behavior.

Psychology also attempts to "fix" behavior.

 

[Integral]

Jericho,

The US seems to be running about a half-dozen deficits right now. There is a fiscal budget deficit ($500 billion in 2008), a large current account deficit ($800 billion), a low personal savings rate (for some definitions of "savings"), a negative national savings rate, and a host of domestic infrastructure problems. Looking on the horizon, there will be major funding problems in both Social Security and Medicare within one generation's time.

Which of these is most important? Least important? Should the Federal government make deficit-reduction a priority? If not, should they do so after the current slowdown subsides? I'd also like your opinion on the trade deficit in particular - is it a self-correcting phenomenon or a symptom of long-term macroeconomic imbalances? If the latter, how long can such imbalances last?

Neither Obama nor McCain will balance the budget anytime in the next four years. It feels like being a deficit hawk is becoming an exercise in futility...

Sorry for all the policy-oriented questions. I'll probably have some theory questions soon enough.

 

[Whomp]

From my perspective, there's some flaws in two pieces of data.

One is retired people are lumped in with wage earning people on savings rate. Ever since the shift in the mid 80s from defined benefit (pension) to defined contribution (IRA and 401k) occurred it meant that consumption continued to count but distributions from IRA's does not count as income (though pensions do) hence skewing the stats towards consumption.

I'm also concerned with the trade data since many multinational companies do business directly through their affliates unlike many foreign countries do with the US.

Personally, the Social Security issue is easy to fix (1.95% increase across the board) but the medicare one is much more complex. My guess is nothing will happen till we're at the abyss (the way gov't always works) and wealthier recipients will have to fend for themselves.

 

[JerichoHill]

I agree with Whomp on the savings rate and trade deficit.

We *could* do something about our budget deficits. We *could* do something on SS. We *could* repeal the Prescription Drug benefit plan and buy us 40 years on Medicare.

Any of those should be a priority. However, I doubt anything gets done until 11:59 and 59 seconds.