Musings On Plausibility

Dale and Craig have sent in their own recent contributions to the Great Plausibility Debate, so I thought that I’d send in something as well because it interests me.

First and foremost, I’d like to advance a definition of what a plausible event is. A plausible event is one which has no alternatives that are substantially more probable. An event can be considered implausible if there is a single alternative (or class of similar alternatives) which is very noticeably more probable than the event in question. A sequence of events (thus an alternate history) is plausible if the plausibility of events in it shows the expected distribution. What I mean by this is that most of the events in the sequence should be plausible as defined above. Implausible/improbable events can and indeed should occur, but as a minority of the total number of events. Imagine it sort of like rolling a six-sided dice, where an implausible event is a one. If you roll the dice many times in a row, ones shouldn’t come up most of the time, but they should come up some of the time. Highly implausible events should still be quite rare, the sort of event that one can look at and admit that it is possible, but that its actual happening would be extremely unlikely. If there are many such highly implausible events in an alternate history, it starts to look ridiculous fairly quickly. Simple statistics indicate that if three events each independently have a 1% chance of happening (in other words not an event beyond belief), then the chances of all three occurring is one in a million.

This is, in fact, a pet peeve of mine and perhaps why I come up with estimates of the plausibility of various alternate histories that differ significantly from those of other people. This may be my mathematical background coming out, but I instinctively view implausibility as multiplicative while many people seem to view it as additive. If I see a sequence of multiple events, each of which is unlikely and overly convenient but still individually within belief, I tend to estimate the plausibility as extremely low. Many people seem to accept most alternate histories unless there is at least one event which they simply cannot believe.

Not only is this view justifiable in the sense of realism, I think that it is usually justifiable in terms of plain ol’ suspension of disbelief and scenario merit as well. Many alternate histories have systematic implausibilities in the “convenient” sense – events turned in a certain way over and over again to produce a desired result. Personally I tend to find this annoying, and perhaps a bit lazy. It’s my belief that a well-designed divergence or two, a few big changes or assumptions, can produce pretty much any scenario that one might want to write about. Even if not technically plausible these can be good thought experiments: "Accepting such and such, what would happen?” Systematic “twisting” of events, however, tends to ruin the whole scenario as a historical extrapolation. It’s unsatisfying to read an alternate history that boils down to “what if this long string of lucky/unlucky breaks and coincidences happened to occur?” It’s also uninformative, because instead of an outlandish assumption or divergence that is treated in a consistent way, the treatment itself is twisted to produce the desired result. All that ends up “counting” is what the end result is used for (such as a story), rather than using the alternate history itself to generate any particular interest.

I think that the ability of implausibility to bring out unusually interesting or exciting characteristics is quite overrated. The most interesting or exciting results from “implausible” scenarios tend to result from what might be better described as impossible scenarios. Alterations to the laws of physics, insertion of supernatural or alien forces, time travel, and the like. Most implausibility I have encountered is either an error, or a deliberate oversimplification to portray something in a way understandable to people who don’t know much about history. While I understand the latter from a standpoint of marketing and accessibility, that doesn’t mean I personally have to enjoy it as much as something that takes aim a bit higher.

In my view, if you want to examine a certain question or tell a certain theme of story (as opposed to something specific like “Nazi-occupied Britain in 1941”), then there should be a plausible alternate history out there that it can be done with. Finding this may require some work and creativity, such as extending a point of divergence further into the past than when you want the change to occur, but it can be done.

I think that there is also a benefit to simply creating a plausible but significantly differing AH with no purpose in mind other than seeing where it goes. I find this an excellent creative exercise, because new themes often present themselves. I can create an alternate history scenario, look at it to see the possibilities, and encounter something that I had never even thought of before. And on top of that, I’ve got a nice plausible scenario all done to base it on, no twisting or “creative temporal engineering” required.

For example, the Atomic League timeline is quite long and complex, and I also think that it is relatively plausible. It wouldn’t be hard to make the basics of the timeline understandable to just about anyone, though. The American Revolution is a recognizable point of divergence, as is a “President for Life”. The basics of the timeline’s history could be distilled into a few pages worth for the reader who doesn’t know much history, providing a good basis for understanding why the modern League world is the way it is. For the avid reader one could insert some of the far greater volume of detail that makes up the timeline in its entirety, and highlight many of the “popular” historical events that went differently or didn’t happen. The timeline is developed in sufficient detail that there are as many points of interest in its history as there are in two centuries of major events in real history.

Probability and Plausibility

My criteria for AH is simply an extension of a standard concept in probability, but I suppose that probably isn’t as obvious to most people as I tend to assume. Let me illustrate, using an example, why I criticize a timeline for having lots of implausible events, but regard a single implausible event as relatively unremarkable.

Since many (most?) POD members are quite familiar with RPGs, let me use an example based on dice. We’re going to use one die, with ten sides. This fits in nicely with my criteria that to call something “implausible”, it should be at least an order of magnitude less likely than some other alternative. Our timeline consists of rolling the die, over and over again. When it comes up 1, an implausible event happens. Any other number is a plausible event. It should be fairly obvious that for any specific event, the plausible outcome is much more likely, but the implausible outcome is not unlikely enough to criticize. A 1 in 10 chance is still pretty significant. So, for any single event, we can obviously say that there is a fair chance that the implausible outcome would actually happen.

The issue becomes more complicated, however, when you consider the whole “timeline”. Let’s say, for example, that we have a “timeline” involving ten major events. These events are major in the sense that they have a big and obvious impact on the final outcome. They’re the kind of events that the author of an AH might want to come out a certain way, in order to produce a desired timeline or story setting. It should be fairly obvious that, in this timeline consisting of 10 die rolls, the average timeline will have 1 implausible event. Roll a 10-sided die 10 times and you can have 1 come up anywhere from 1 to 10 times – but the most likely result is that it will come up just once.

Now, how might we apply the concept of plausibility to this timeline as a whole? Well, the information we have is that we have a certain number of events, each of which has outcomes of different likelihood. Namely, there are 10 events and in each event a plausible outcome is 9 times more likely than an implausible outcome. We can define the plausibility of the timeline in terms of how many plausible events are in it – because it is more likely that there will be 1 than 2, more likely that there will be 2 than 3, and so on.

In fact, I’m going to include some numbers to show how dramatically probability (and thus, in this simple example, plausibility) changes as you increase the number of implausible events. It is 35% likely that there will be 0 implausible events. It is 39% likely that there will be 1 implausible event, 19% likely that there will be 2, 6% likely that there will be 3, and 1% likely that there will be 4. These numbers already add up to 100% due to rounding error, thus we can see that the likelihood of anywhere from 5 to 10 implausible events is small, even all together. In fact, the probability of 8 implausible events is 1 in 36 million, and the probability of 10 plausible events is 1 in 10 billion.

Because we have the probabilities of all possible events in this example, the relative probabilities are obvious too. If anywhere from 0 to 3 events out of the 10 have implausible outcomes, the timeline is plausible. With 4 implausible events, you’ve already got a timeline which is an order of magnitude less likely than other outcomes. A few more than that, and you’ve entered the territory of ridiculously implausible timelines. And that is when the “implausible” individual events are in themselves not all that unlikely, and a relatively short sequence of events has been considered.

From this analogy, it should be possible to see how I call some timelines implausible without calling OTL implausible. OTL has plenty of implausible events, but about as many as you’d expect from random selection. To use the example, OTL is a timeline pretty close to the “roll a 1 only about 10% of the time” standard. Many ATLs, on the other hand, have divergent histories where many, or even most, of the major events in the ATL are implausible. The more implausible events you put in, the more the timeline itself slides into implausibility.