100-yard-line model for conversion

Brian Tomasik · by **Brian Tomasik** on 2012-12-27T06:58:00

Summary:
Naive estimators of veg conversion are in fact unbiased estimators of your total counterfactual contribution to veg conversion, at least according to one simple model.

Background:
A comment on "The power of effective activism":

Roman Duda:

One small point: “Supposing each person he convinces remains vegetarian for on average 25 years over their life (they were mostly university students), the number of animals saved from a life in a factory farm is closer to 10 million” Doesn’t this assume that each person Joe convinces wouldn’t have become vegetarian if it hadn’t been for Joe? But surely Joe is not the only force shaping individuals towards becoming vegetarians. So if Joe convinces someone to become vegetarian, he may ‘just’ be bringing forward in time when that person becomes vegetarian. This is likely to be the case for at least some of the individuals that Joe convinces. So the estimate as it stands is probably overly optimistic.

My reply:

Brian Tomasik:

As far as Roman’s point, “surely Joe is not the only force shaping individuals towards becoming vegetarians,” here’s a comment I wrote to a friend a few weeks ago:

“Yes, some of the people we convince were already on the border, but there might be lots of other people who get pushed further along and don’t get all the way to vegism by our influence. If we picture the path to vegism as a 100-yard line, then maybe we push everyone along by 20 yards. 1/5 of people cross the line, and this is what we see, but the other 4/5 get pushed closer too. (Obviously an overly simplistic model, but it illustrates the idea.)”

Here’s an elaboration on the 100-yard-line model for veg conversion. Say there are K influences encouraging people toward vegism (e.g., The Humane League’s veg ads, work by other veg groups, movies like Food, Inc., influence by friends, religious sentiments, etc.). Say there are N total veg conversions due to all these factors combined. Let p_i, i = 1, …, K be the relative amount by which each influence pushes people along the 100-yard line. For example, if The Humane League’s veg ads push people twice as far or push twice as many people as hearing news stories about factory farming does, then p_{THL} = 2 p_{news stories}. Let f_i = p_i / (sum_i p_i). If the influences come in a random order (e.g., sometimes veg ads happen before influence by friends and sometimes influence by friends happens first), then the number of observed conversions due to the i’th influence will have the expected value f_i * N, because, for example, an influence that pushes people twice as far along will result in them crossing the finish line twice as much, and an influence that reaches twice as many people will result in twice as many crosses of the finish line. In other words, in apportioning responsibility for veg conversions, the actual number of people that you cause to cross the finish line is an unbiased estimator of your fractional causal contribution to all N veg conversions.

The intuition is that, yes, some of the people you convert with veg ads would have gone veg due to other reasons. But some of the people you don’t convert will now go veg due to something else because you helped them along the road.

xodarap · by **xodarap** on 2012-12-29T01:30:00

Brian, I think this is a clever idea, but I'm not as convinced as I was at first. Consider an extreme example: everyone will go vegan the next day after Joe's outreach, regardless of what he does (100 yards are added to their veganism, as it were).

Figuring out the exact expectation proved daunting, but I made a small R program to play with some values. In general, it seems like the benefit is significantly less than the naive calculation:

Code: Select all

brian = function() {
  # Model people as in the range [0,inf]
  # If they are > 1, then they are vegetarian
  # Interventions (like leafletting) make people more likely to go veg
  # by a uniform offset in [0, .01]
  factual = runif(1000)
  counterFactual = factual
  # VO's intervention
  factual = factual + runif(1, min=0, max = .01)
  factVeganYears = sum(factual > 1)
  counterFactVeganYears = sum(counterFactual > 1)
  
  for(year in 1:20) {
    change = runif(1, min = 0, max = .01)
    factual = factual + change
    counterFactual = counterFactual + change
    
    factVeganYears = sum(factual > 1) + factVeganYears
    counterFactVeganYears = sum(counterFactual > 1) + counterFactVeganYears
  }
  print(factVeganYears)
  print(counterFactVeganYears)
}

(Output varies, but is e.g. 935 vs. 1010)

You could argue that this discounts the effects of the new vegans introducing others to veganism etc.

Anyway, I certainly think even with some discounting of the naive calculation, VO is still a great organization!

Brian Tomasik · by **Brian Tomasik** on 2012-12-29T14:00:00

Very interesting, xodarap. My reasoning was slightly flawed because I was looking at total people converted vs. total contribution toward doing that conversion, but because (in this simple model) conversion is binary, extra pushing along after conversion doesn't help, so regardless of who did that last amount of pushing, the fact remains that we could have done less pushing and still gotten the same effect.

The effect of any given intervention is still bigger than Roman's comment suggested, because it's not as though the only effect is (# of people we see converted) - (# who would have converted without us). There are also people we don't see being converted who then are converted by something else but wouldn't have otherwise.

Maybe the best way to look at the situation is to forget about which group/influence is doing which part of the conversion and just ask, if we push everybody along by an extra y yards, how many more conversions will that produce? Since some people would already go past the 100-yard-line without the extra y yards, the number is less than y/100. In fact, assuming people are uniformly distributed, the fraction is something like (y/100)*(fraction of people who wouldn't have been converted without you), although this isn't quite right if we assume that everyone is already being pushed along. At this point things become sensitive to the details of the model, but the point is that it seems like the counterfactual impact isn't that much lower than the naive estimate.

xodarap · by **xodarap** on 2012-12-30T02:25:00

You could keep the linearity in your model by pointing out that people who go veg are more likely to convince others to go veg. Say, if I had a vegan score of 1.5, this is equivalent to me being vegan, plus adding .5 to my girlfriend's score.

100-yard-line model for conversion

100-yard-line model for conversion

Re: 100-yard-line model for conversion

Re: 100-yard-line model for conversion

Re: 100-yard-line model for conversion