This sounds like regular risk aversion, which is normally easy to model by transforming utility by some concave function. How do you show that there's an actual violation of the independence axiom from this example? Note that the axioms require that there exist a utility function u :: outcome -> real such that you maximise expected utility, not that some particular function (such as the two graphs you've drawn) actually represents your utility.
In other words, you haven't really shown that "to prefer action A, with its attendant distribution of outcomes, to action B with its distribution, is to violate the axiom" since the two distributions don't have the form ApC, BpC with A≅B. Simply postulating that the expected utilities are the same only shows that that particular utility function is not correct, not that no valid utility function exists.
This sounds like regular risk aversion, which is normally easy to model by transforming utility by some concave function.
Assuming you privilege some reference point as your x-axis origin, sure. But there's no good reason to do that. It turns out that people are risk averse no matter what origin point you select (this is one of the major findings of prospect theory), and thus the concave function you apply will be different (will be in different places along the x-axis) depending on which reference point you present to a person. This is clearly irrationa...
It's been claimed that increasing rationality increases effective altruism. I think that this is true, but the effect size is unclear to me, so it seems worth exploring how strong the evidence for it is. I've offered some general considerations below, followed by a description of my own experience. I'd very much welcome thoughts on the effect that rationality has had on your own altruistic activities (and any other relevant thoughts).
The 2013 LW Survey found that 28.6% of respondents identified as effective altruists. This rate is much higher than the rate in the general population (even after controlling for intelligence), and because LW is distinguished by virtue of being a community focused on rationality, one might be led to the conclusion that increasing rationality increases effective altruism. But there are a number of possible confounding factors:
So it's helpful to look beyond the observed correlation and think about the hypothetical causal pathways between increased rationality and increased effective altruism.
The above claim can be broken into several subclaims (any or all of which may be intended):
Claim 1: When people are more rational, they're more likely to pick their altruistic endeavors that they engage in with a view toward maximizing utilitarian expected value.
Claim 2: When people are more rational, they're more likely to succeed in their altruistic endeavors.
Claim 3: Being more rational strengthens people's altruistic motivation.
Claim 1: "When people are more rational, they're more likely to pick their altruistic endeavors that they engage in with a view toward maximizing utilitarian expected value."
Some elements of effective altruism thinking are:
Claim 2: "When people are more rational, they're more likely to succeed in their altruistic endeavors."
If "rationality" is taken to be "instrumental rationality" then this is tautologically true, so the relevant sense of "rationality" here is "epistemic."
Claim 3: "Being more rational strengthens people's altruistic motivation."
Putting it all together
The considerations above point in the direction of increased rationality of a population only slightly (if at all?) increasing the effective altruism at the 50th percentile of the population, but increasing the effective altruism at higher percentiles more, with the skewing becoming more and more extreme the further up one goes. This is in parallel with, e.g. the effect of height on income.
My own experience
In A personal history of involvement with effective altruism I give some relevant autobiographical information. Summarizing and elaborating a bit:
How about you?