Why Flip a Coin?: The Art and Science of Good Decisions

Rating:
Summary: Good, but with some flaws
Review: ...I found it interesting, informative, and readable, but I do believe that the author carries his belief in cost effectiveness too far. It appears he would approve of the car company that declined to fix gas-tank flaws they discovered in a vehicle, because it was cheaper to pay off injury lawsuits than to conduct a recall. Still worth reading. The author does explain himself in detail, and you will understand the points he wanted to make in the book.

Rating:
Summary: I enjoyed reading this a lot.
Review: I really enjoyed reading this book. But, trust me, don't explain the dating game problem with your girlfriend!

The book starts off discussing the dating game. How do we find the best mate? What the heck does mathematics have to do with that? If you want to select the best spouse (rated by some criteria you've chosen) from a group of one hundred willing applicants, you have several ways to approach this decision.

In the game, you are only allowed to date each potential candidate once. If you reject the candidate, the candidate lost forever, as he/she joins the monastery. How do you make your decision?

If you just select the first potential spouse who comes along, you only have a 1/100 chance that you will select the best. That's not very good odds, as many people have discovered! Suppose however, that you date the first ten potential spouses as a sample. You then use this sample as a guide to what's out there. As Lewis writes, that's what dating's all about!

By selecting the next potential spouse (after the first ten) who ranks higher than any of the sample of ten, you now have a 1/4 chance of getting the best. That's a far better chance than selecting at random!

But, there are two ways your strategy could fail. First, the best spouse might have been within the group of the first ten. Then, you missed the best spouse. Second, the eleventh person chosen might be better than any of the first ten, but he/she might not be that good either. In fact, the candidate could be the eleventh worst.

The question becomes: How big should my sample population be to maximize the chances of getting the best spouse? It turns out to be 36. You date 36 potential spouses and choose the next one who ranks higher than any of the first 36. This gives you a 1/3 chance of getting the best.

However, another question is: Just how important is it to select the best mate from the lot? Would not one of the top five be adequate? Especially, if you minimize the chances of winding up with a real dud? By playing more conservatively and only sampling the first 30, your chances of getting the best decreases only slightly, but your chances of getting either the best or the second best increases to 1/2.

By understanding the dating game, you've gone from having only a 2% chance of winding up with one of the top two spouses to having a 50% chance of getting one of the top two spouses!

Of course in real life we face other problems, such as idealizing someone we dated long ago. We might bump them up to an unrealistically high rating against whom no one can compete! Maybe, some potential spouses just won't date us. And, it wouldn't go over too well to tell a potential spouse "I really like you a lot but you're only number 28. I'm waiting till I've dated 30 to commit!" Nonetheless, in our example, we can greatly increase our decision-making above the 1/100 chance of getting the best by random selection.

So much for the metrics of mating. Even without understanding the full mathematical details, we can benefit from seeing the logic of sampling some of the population before making a choice. In fact, "Why Flip A Coin?" doesn't work out the complicated mathematics. It just states the odds to make the point. We don't need to be able to work out detailed mathematics to be able to make better decisions, in general. We do need to think about the logical process used in making the decision.

Lewis does a great job of explaining hedging. He uses a football pool as an example. There are only two teams, The Ducks and The Geese. And, there is only one other person, Fred, betting. Assume each team is equally likely to win.

Fred puts $1 into the pool and chooses The Ducks. What do you do? You toss in a buck for The Ducks, and you toss in a buck for The Geese. You bet on both teams. You hedge. There is now $3 in the pot.

If The Ducks win, $3 is split between you and Fred. You get $1.50 for a loss of $0.50. But, if The Geese win, you collect $3.00, for a gain of $1.00. Because each team has an equal chance of winning, your expected result is:

Expected Winnings = 1/2 ($1.50) + 1/2 ($3.00) = $2.25 which is more than the two dollars you wagered. In fact, the expected return here is 12.5%. Via hedging, despite having no superior knowledge of which team will win, in the long run, you come out ahead.

As Lewis writes, don't go betting your money on football pools just because you know this! Someone who posses superior knowledge of which team is most likely to win in the real world has the advantage.

Much of "Why Flip A Coin?" is devoted to group decision making and the social implications of the way group decisions are made. In particular, the book discusses voting, the electoral college, and how difficult it is to translate the wishes of a group of people into a collective decision.

Rating:
Summary: A valuable book
Review: I reviewed this book earlier, but wish to answer the author's question (also via review comment) about the mathematical errors I previously mentioned. I also wish to amend my prior review a bit. Now that a few months have passed since I read the book, I have found some of its ideas very valuable and insightful. His comments on group decisions should be required reading for anyone involved in such a task. As a voter choosing a president, a committee member at a job trying to decide what course the company should take, or even as an individual who 'just can't decide' between several tempting choices, the principles of this book are vitally important. However, one example of a math error follows. Professor Lewis talks about the 'random walk' of stock prices on page 144 of the paperback version in chapter 18. Perhaps I have misunderstood the concept, but as I understand it, his premise is this: if there is a 50% chance that a stock will go up by 10% of its current value, and a 50% chance that it will go down by 10% of its current value, then "If a stock happens to have gone up 10 percent, the next 10 percent will be larger than if it had gone down, and that adds up to gains in the long run. So a random walk of this kind is... ...tilted toward higher averages." In the long run, I see a random walk of this type tending toward zero. Imagine a simple example: starting with a stock worth 100 dollars, the value then goes up 10% followed by a decrease by 10%. The first change (increase) is by 100 x 0.10 = 10 dollars, so you are left with a 110 dollar stock. The second change (decrease) is by 110 x 0.10 = 11 dollars, so you are left with a 99 dollar stock, a definite trend down! What about the long term? It was a simple matter to generate a spreadsheet with 5000 random steps up or down by 10% of the value of the previous step, and graph the stock price versus number of random moves. Push the recalculate key as much as you want, and you will find that in almost every run of 5000 steps, you end up with a stock valued very near zero. Take note, there are usually some interesting excursions in the price, sometimes to quite high a level, but given enough steps, it always comes back to near zero. Thus, this scenario is not biased toward an increasing trend, but rather just the opposite. Nevertheless, read the book!

Rating:
Summary: NOT for actuaries & experts in statistical decision theory
Review: The inevitability of decision making means it pays to understand how decisions are made, ergo decision science. Using examples gleaned from everyday life, physicist H.W. Lewis explains what decision science has discovered about the rules that govern good, and not-so-good, decision-making.

This book is not intended for actuaries and those already expert in statistical decision theory. It is intended to help the rest of us improve our understanding of decision science, to become more inquisitive about how decisions are made, both by us and for us, and to function a little more effectively, both as individuals and as members of society.

The author is Professor Emeritus in Physics at the University of California, Santa Barbara. In 1991, he received a Science Writing Award from the American Institute of Physics. He is a member of the Advisory Committee on Nuclear Facility Safety.

Reviewed by Azlan Adnan. Formerly Business Development Manager with KPMG, Azlan is currently managing partner of Azlan & Koh Knowledge and Professional Management Group, an education and management consulting practice based in Kota Kinabalu. He holds a Master's degree in International Business and Management.

Rating:
Summary: It helps to be American...
Review: This is a book about the process of making decisions. It covers quite a broad range of topics from individual decision making to group decisions. Both qualitative and quantitative perspectives are considered. Good decisions do not necessarily result in good outcomes. Instead the decision maker is responsible for making the best decision possible with the information on hand at the time. This usually results from an assessment of the projected consequences and the probability of various outcomes.

I like the book because it is easy to read and the author laces the text with some very humorous cynicism. The book covers a diverse number of topics from dating, to gambling, to investing to war. Unfortunately the book is most definitely targeted at the American market. The book includes discussion on American law, the Constitution and American sports. Occasionally I found my eyes glazing over because I couldn't find any broad relevance in the material. This only occurred a small percentage of the time much of the book is very generalisable to anyone faced with making a decision.

Overall the book was a highly enjoyable read. Thoroughly recommended if you would like to improve your decision making or would just like a good intellectual exploration of the process of making sound decisions.