The press article suggests that's not the case, but while the odds of being helped go up with more people, that doesn't mean the probability for any given person is going up. Think of it this way, if you flip a coin, and "heads wins", you have a 50% chance of winning. If you roll a die, and "1 wins", you only have a 1 in 6 chance of winning. But, if you get to roll the die 10 times, and all you need is for one of them to be a 1, then your odds of winning with the die are better than the odds with a single coin flip.
What I've done is calculated the odds as per the findings of the research article (as above). As we see, the probability of 1 or more people helping goes up as there are more people. The probability with 1 bystander is approx 52%, so the probability of not being helped is about 48%. Now, if adding more bystanders does not decline the odds of an individual helping or not, then the odds of nobody helping when there are 2 people would be 0.482, so the probability of being helped would be 1-0.482 (around 77.3%). But, if adding more people does reduce the odds of each person helping ("someone else will do it"), then there would be less than a 77.3% chance of being helped when there's 2 bystanders, and if there were "safety in numbers", so the probability of any individual helping increases with more bystanders, then we would have a greater than 77.3% chance of being helped. And if adding more people has no impact on the probability of each person helping, then 77.3% it is.
Turns out, the observed rates are reduced, which tells us that adding more bystanders does reduce the probability of an individual helping, but given the increase in people present, the probability that at least one of them helps continues to grow. The "bystander effect" does happen (the probability for an individual goes down - someone else will do it), but the number of bystanders still means the probability of being helped goes up.
Here's the plot for comparison (the orange data is what would happen if adding more bystanders doesn't change the probability for an individual to intervene; the blue line represents the article's analysis, and we see that what is observed is less, which means the increase in crowd size is reducing the probability for each individual to get involved; notice, the predictions are of course identical for 0 and 1 bystanders; noone is there to help in the former, and there are no additional bystanders to reduce the probability when you're the only one present). The space between the two curves represents the "bystander effect".
Anyway, just thought I would share that as the bystander effect is one of those things that occasionally gets a lot of press, but the way in which it gets presented is so often badly mangled that it sounds like the probability of anybody helping goes down as the crowd size increases. it's not, it's the probability of any specific individual helping that goes down, the crowd numbers make up for that.
Oh, and also, it may not really be best described as "someone else will do it", the same thing would happen if we think of it as "somone else already has done it".
- Jeff
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