Summation of terms in survival function giving negative probability The following expression represents a survival function for a group size (n), where survival is a percentage on a scale of 0 to 100.
$$
p(x) = 100 - \beta(x \cdot x) = 100 - \beta\sum_{i=1}^{n}x_i^2
$$
According to this paper, plotting this expression looks as follows:

But isn't this only true if the summation leads to something equal or less than 1? Anything more than 1 in the summation will lead to negative probability (impossible) of survival.
For example, using a group size of 5, and an "action" value of 0.75, leads to a sum of:
(0.75^2) + (0.75^2) + (0.75^2) + (0.75^2) + (0.75^2) = 2.8125

...which gives a p(x) of (if using a beta of 100):
100 - (100*2.8125) = 100 - 281.25 = -181.25

Based on the plot by the authors, it seems as though the only way to get their results is if the group size (n) is 1. But this wouldn't be a group.
What am I missing? Am I doing the summation wrong?
 A: No, you are not misunderstanding anything. As the authors say immediately before this figure:

Note in (2) that it is possible for some actions x to result in p(x) < 0, which is interpreted to mean that the group has no chance of survival.

You are also correct that Figure 1 is a plot of the survival probability for a single individual. Note that there is no summation in the image title. In general the different individuals in a group will have different $x$ values, and so an accurate plot of the survival probability for a group of 2 would be a 3-dimensional image. For larger groups an accurate plot would be impossible to visualize. A plot of the survival function for 1 individual might not be what you hoped to see, but it does illustrate the proposed mechanism. In particular, the smooth quadratic relationship between $x$ and the survival probability.
Finding negative estimated probabilities is a general problem with "linear probability models". This problem was recognized very early on, so models using non-linear link functions like logit or probit links are much more common. But sometimes linear models are still useful.
