I think the example given to show the irrationality of leximin in certain situations doesn’t do a good job of distinguishing its failings from maximin. To usefully illustrate the difference between the two I believe a another state is required with even worse outcomes for both acts (e.g. $0). This way the worst outcomes for both acts would be equal and so the second worst outcomes (a1:$1, a2:$1.01) would then be compared under the leximin strategy leading to the choice of a2 as the best act again with the acknowledgment that you miss out on the opportunity to get $10,001.01
I think the example given to show the irrationality of leximin in certain situations doesn’t do a good job of distinguishing its failings from maximin. To usefully illustrate the difference between the two I believe a another state is required with even worse outcomes for both acts (e.g. $0). This way the worst outcomes for both acts would be equal and so the second worst outcomes (a1:$1, a2:$1.01) would then be compared under the leximin strategy leading to the choice of a2 as the best act again with the acknowledgment that you miss out on the opportunity to get $10,001.01