I feel like you’re trying to take something informal and formalize it, and some of the features of your formalization don’t seem motivated by the informal version.
If an informal claim about economics doesn’t translate readily to a formal claim, then it’s not even wrong. Informal language games are fine in many contexts, but Elizabeth’s posts tend to be about careful fact-gathering and scrutinizing sources for accuracy, so I think it’s OK to apply that standard to her work.
My guess would be something like “unstable”, in the sense that once it goes away, there’s no particular reason to expect it to come back.
This would only be true if
a) The TPE outweighs more fundamental factors, meaning that it’s hard for a lower-ranked choice to become the top choice, merely due to the TPE.
For example, Facebook is useful primarily because so many people are on it. It would be hard for a direct competitor to attract a user base no matter how much better the underlying software is. There is a clear way to rank all the alternatives in terms of quality, but there’s a huge cliff between 1st and 2nd place that exists merely due to the TPE.
b) Random noise outweighs more fundamental factors (or there’s no fundamental factors at all), meaning that the differences between lower-ranked choices is obscured by chance. There is no clear way to sort lower-ranked alternatives in terms of quality.
For example, you have no knowledge of horse racing. But you happen to hear that the Mafia given Black Beauty a drug that makes her 5% faster (TPE), making her slightly more likely to win the Kentucky Derby, but not guaranteeing her victory. If the Mafia changes its mind and decides to drug Seabiscuit instead, there’s no clear reason to expect that they’ll change their mind a third time. Even if they do, there’s no reason to think they’ll change their mind back and drug Black Beauty, rather than doping Secretariat or Man ’O War. The Mafia is unlikely to change its mind, so you assume that Black Beauty has a small but durable edge.
These two examples illustrate that the TPE has several factors.
It can have a large or small importance relative to fundamental factors (large in the case of Facebook, small in the case of Black Beauty). A small difference implies fragility, large differences imply durability.
It can be endogenous (Facebook’s TPE is due to it having the most users, so the fact that it’s in 1st place helps anchor it in 1st place) or exogenous (Black Beauty’s TPE is due to outside intervention, and it’s not clear how capricious the Mafia will be in changing this choice). Exogenous factors are fragile, endogenous factors are durable.
And the non-TPE fundamentals of the options can be well-ordered (as in the case of Facebook’s software quality relative to its competitors) or unordered (as in the case of the horse racing neophyte at the Kentucky Derby). Unordered fundamentals mean that the choice selected for the top spot is arbitrary, so that having held the top spot confers no special advantage in regaining it if it is lost. Unordered fundamentals imply fragility, well-ordered fundamentals imply durability.
All of these factors vary empirically. No matter whether “fragility” referred to one, two or all three of these factors, it’s clear that fragility and durability exist on a spectrum and may vary widely on a case-by-case basis.
Indeed, Elizabeth says
Tallest pygmy effects are fragile, especially when they are reliant on self-fulfilling prophecies or network effects.
It’s not clear to me that “self-fulfilling prophecies or network effects” are inherently fragile. The advantage that Facebook gains due to the size of its user base is an example of a network effect that is durable in all three senses of the term as I’ve defined it.
This matters. If we cultivate “TPEs tend to be/are inherently fragile” as a heuristic, it will encourage people to look at problems like “how to make a social media company that’s bigger than Facebook” as a technical problem. “If you build it, they will come.” Well, no, not necessarily. Facebook’s TPE is a big moat. In fact, I’d offer an alternative heuristic:
The more obvious the TPE, the more likely it is to be durable.
If an informal claim about economics doesn’t translate readily to a formal claim, then it’s not even wrong. Informal language games are fine in many contexts, but Elizabeth’s posts tend to be about careful fact-gathering and scrutinizing sources for accuracy, so I think it’s OK to apply that standard to her work.
This would only be true if
a) The TPE outweighs more fundamental factors, meaning that it’s hard for a lower-ranked choice to become the top choice, merely due to the TPE.
For example, Facebook is useful primarily because so many people are on it. It would be hard for a direct competitor to attract a user base no matter how much better the underlying software is. There is a clear way to rank all the alternatives in terms of quality, but there’s a huge cliff between 1st and 2nd place that exists merely due to the TPE.
b) Random noise outweighs more fundamental factors (or there’s no fundamental factors at all), meaning that the differences between lower-ranked choices is obscured by chance. There is no clear way to sort lower-ranked alternatives in terms of quality.
For example, you have no knowledge of horse racing. But you happen to hear that the Mafia given Black Beauty a drug that makes her 5% faster (TPE), making her slightly more likely to win the Kentucky Derby, but not guaranteeing her victory. If the Mafia changes its mind and decides to drug Seabiscuit instead, there’s no clear reason to expect that they’ll change their mind a third time. Even if they do, there’s no reason to think they’ll change their mind back and drug Black Beauty, rather than doping Secretariat or Man ’O War. The Mafia is unlikely to change its mind, so you assume that Black Beauty has a small but durable edge.
These two examples illustrate that the TPE has several factors.
It can have a large or small importance relative to fundamental factors (large in the case of Facebook, small in the case of Black Beauty). A small difference implies fragility, large differences imply durability.
It can be endogenous (Facebook’s TPE is due to it having the most users, so the fact that it’s in 1st place helps anchor it in 1st place) or exogenous (Black Beauty’s TPE is due to outside intervention, and it’s not clear how capricious the Mafia will be in changing this choice). Exogenous factors are fragile, endogenous factors are durable.
And the non-TPE fundamentals of the options can be well-ordered (as in the case of Facebook’s software quality relative to its competitors) or unordered (as in the case of the horse racing neophyte at the Kentucky Derby). Unordered fundamentals mean that the choice selected for the top spot is arbitrary, so that having held the top spot confers no special advantage in regaining it if it is lost. Unordered fundamentals imply fragility, well-ordered fundamentals imply durability.
All of these factors vary empirically. No matter whether “fragility” referred to one, two or all three of these factors, it’s clear that fragility and durability exist on a spectrum and may vary widely on a case-by-case basis.
Indeed, Elizabeth says
It’s not clear to me that “self-fulfilling prophecies or network effects” are inherently fragile. The advantage that Facebook gains due to the size of its user base is an example of a network effect that is durable in all three senses of the term as I’ve defined it.
This matters. If we cultivate “TPEs tend to be/are inherently fragile” as a heuristic, it will encourage people to look at problems like “how to make a social media company that’s bigger than Facebook” as a technical problem. “If you build it, they will come.” Well, no, not necessarily. Facebook’s TPE is a big moat. In fact, I’d offer an alternative heuristic:
The more obvious the TPE, the more likely it is to be durable.