Percentage Potshots

Over the years, I've had a few recurrent fights in situations where I wanted to use raw values rather than percentages, but was stared as as if I was crazy. Yes, I know that sounds boring, but please bear with me.

Situation 1: Tipping a waiter. As you know, the standard practice is that you tip the waiter a percentage of the bill - let's say 10%. But it's always seemed to me that this unfairly discriminates against waiters who work in cheap restaurants. They're basically doing the same job as the waiters in posh restaurants, but a) they're probably getting a lower basic wage anyway, so b) by tipping them a percentage of your lower bill you are diddling them twice over. Surely it would be fairer to decide what amount constitutes a reasonable tip, adjust it a bit depending on whether the service is good or bad, and leave them that. I used to argue this point quite regularly, but gave up after a while because I found that I couldn't convince anyone that it made sense.

Situation 2: Deciding how many student papers need to be double-marked for the purposes of moderation. Standard practice in my place of work was for many years to prescribe a percentage of the scripts submitted - let's say 15%. Thus, you would end up double-marking a lot more scripts on a course with a high number of students than on a course with only a few. Every year, I would argue that for sampling purposes (at least of this type) what matters is the sample size, not the percentage of the population represented by the sample. (If you're not clear why this makes sense, there's a handy discussion here.) Every year, my colleagues would wait for me to calm down, and then take no notice.

Okay, perhaps in the grand scale of things neither of these things matters so much. Who cares about waiters or students, after all? (Actually, they're often the same people.) But twice in the last 24 hours I have heard people defending the large bonuses paid to bankers using the same kind of specious argument. In short, it goes like this: "X makes his living investing large sums of other people's money. If he is successful and his deals earn the bank a profit of $5,000,000 then it's only fair that he should be rewarded with a percentage of that profit." Not, note, rewarded with a few thousand extra in his pay packet. Not even with a percentage of his basic salary, but a percentage of the profit he has "earned". In other words, it's the posh waiter argument all over again, but with a posh waiter who serves platefuls of diamonds and gold bullion rather than beef wellington with grilled asparagus.

Do the banker apologists actually believe what they're arguing, I wonder? It would take only a very basic understanding of maths and statistics (which is all I have, if that) to see that their argument is tendentious at best. And yet - I remember the incomprehension of my colleagues; I think of the disbelieving faces of my dining companions of yore. These weren't stupid people in the ordinary way. And after all, that is the way we tip waiters, in the Square Mile as elsewhere. So, maybe they really do think it's a good argument - because they desperately want it to be one, and because let's face it, on the evidence of the last couple of years they aren't much cop with numbers.

Percentage Potshots

Over the years, I've had a few recurrent fights in situations where I wanted to use raw values rather than percentages, but was stared as as if I was crazy. Yes, I know that sounds boring, but please bear with me.

Situation 1: Tipping a waiter. As you know, the standard practice is that you tip the waiter a percentage of the bill - let's say 10%. But it's always seemed to me that this unfairly discriminates against waiters who work in cheap restaurants. They're basically doing the same job as the waiters in posh restaurants, but a) they're probably getting a lower basic wage anyway, so b) by tipping them a percentage of your lower bill you are diddling them twice over. Surely it would be fairer to decide what amount constitutes a reasonable tip, adjust it a bit depending on whether the service is good or bad, and leave them that. I used to argue this point quite regularly, but gave up after a while because I found that I couldn't convince anyone that it made sense.

Situation 2: Deciding how many student papers need to be double-marked for the purposes of moderation. Standard practice in my place of work was for many years to prescribe a percentage of the scripts submitted - let's say 15%. Thus, you would end up double-marking a lot more scripts on a course with a high number of students than on a course with only a few. Every year, I would argue that for sampling purposes (at least of this type) what matters is the sample size, not the percentage of the population represented by the sample. (If you're not clear why this makes sense, there's a handy discussion here.) Every year, my colleagues would wait for me to calm down, and then take no notice.

Okay, perhaps in the grand scale of things neither of these things matters so much. Who cares about waiters or students, after all? (Actually, they're often the same people.) But twice in the last 24 hours I have heard people defending the large bonuses paid to bankers using the same kind of specious argument. In short, it goes like this: "X makes his living investing large sums of other people's money. If he is successful and his deals earn the bank a profit of $5,000,000 then it's only fair that he should be rewarded with a percentage of that profit." Not, note, rewarded with a few thousand extra in his pay packet. Not even with a percentage of his basic salary, but a percentage of the profit he has "earned". In other words, it's the posh waiter argument all over again, but with a posh waiter who serves platefuls of diamonds and gold bullion rather than beef wellington with grilled asparagus.

Do the banker apologists actually believe what they're arguing, I wonder? It would take only a very basic understanding of maths and statistics (which is all I have, if that) to see that their argument is tendentious at best. And yet - I remember the incomprehension of my colleagues; I think of the disbelieving faces of my dining companions of yore. These weren't stupid people in the ordinary way. And after all, that is the way we tip waiters, in the Square Mile as elsewhere. So, maybe they really do think it's a good argument - because they desperately want it to be one, and because let's face it, on the evidence of the last couple of years they aren't much cop with numbers.