The bigger problem for utilitarianism (though not in this scenario) is that it fudges the detail of maximisation. In mathematics, one cannot maximise two different functions of the independent variables at the same time without also specifying an acceptable trade-off between them. For instance, "Greatness of view" (perhaps measured by straw polls of observers) and "% of time free from rain" are functions of X and Y co-ordinates on a tourist map, when averaged over the long term. One cannot maximise both at once, because the "awesome view" and "dryness" functions will each have their own local maxima and minima (hills and valleys) which in general will be in different places. So to talk of "the greatest good for the greatest number" (Bentham), trying to maximise both "good" and "number" with no specified trade-off, is a total fudge. There may be an action which is spectacularly good for 30% of the people, pretty good for 60%, OK for 80% and utterly rotten for the remaining 20%. Another action may be spectacularly good for nobody, very good for 55%, good for 75%, acceptable for 90%, bad for 5% and very bad for 5%. Which is the better course under Bentham? There is no way to determine the answer - the Bentham formulation is conceptually flawed.
Consider the third action of a decree "Everyone whose name begins with a vowel shall donate all they own into a pot that will be redistributed to those who begin with a consonant". Most people are winners here. Tough on the minority - but who cares about them, they're not "the greatest number".
Mrs Thatcher succeeded in successive elections because she constructed a solid, successful "coalition of the contented" covering around 40%-45% of the population who did pretty well under her (a few very richly so), and that was enough to enable the formation of guaranteed majorities under the first past the post system. But her policies were perceived as calamitous for an equal or somewhat greater number of people (whose candidates to vote for were split into two substantial and competing camps). She was hated as much (or more) as she was adored in the polarised society that her policies created.
As with statistical significance, all we can do under a utilitarian ethic is specify the number we are trying to satisfy (eg 95%) and maximise the good of that chosen group.
I would also argue it is better to minimise the distress of the worst-off 95%, not to maximise the pleasure of the best-off 95%: not the same thing at all (the two groups differ, as do their outcomes).
But why 95%? Why not 90%, or 50%, or one of the Lanchester values for oligipolies?
Utilitarianism is a total fudge if it does not address the measurement question. There is a pretence of serving the greatest possible good with no real attempt actually to do so.