The following points, I believe, should be important for hedonists when it comes to assessing policies or broader political changes in general. I should, however, say that the first point is not strictly a hedonist point, but, rather, a point that I think everyone should subscribe to. Point 2 and 3 are probably less controversial among other hedonists than point 4. Also, consider this list as a work in progress…
A democratic government is the only legitimate form of government (although not possible to achieve under all circumstances). The citizens should have ample opportunities to participate in political life and form reasoned opinions. All political measures that deprive people of the possibilities of learning more about politics or that make it difficult for people to vote or participate in other ways should be viewed with severe suspicion. Furthermore, the democratic system should be based on simple majority rule (for ordinary legislation) and fair multi-parti representation (which, for instance, precludes first-past-the-post systems).
A central application of the hedonist philosophy is that economic redistribution is necessary, since the rich would not be substantially unhappier if they were to become somewhat less rich, whereas there are many poor people who would benefit substantially, in terms of happiness, if they were to be lifted out of poverty. Needless to say, any scheme of redistribution must be adapted to the present economic circumstances, such as the prevalence of egoism among the rich (and, to some extent, among the poor) or the degree of globalization. In any case, a robust welfare state seems to be the best way we have seen so far of giving common people a decent amount of economic security. Generally, all out socialism (in the sense of common ownership of the means of production) is not a realistic way to reach the goals asserted here.
3. Reforms and public planning
Although the combination of an income redistribution scheme and private business can provide people with the means they need to improve their lives, politics can always step in to promote other kinds of reforms that raise quality of life. Things like paid vacation, shorter workdays and parental leave cannot simply be left to bargaining between employers and employees. There is also the case of public amenities like parks, museums, libraries, and sports facilities. Theoretically, these things can be provided by private firms, but so far, experience has not shown that private provision works better than what we have in most developed nations. A hedonist should welcome all ideas about new ways to improve quality of life through political reforms and public planning.
4. Individual development
To break out from the pressures of social control is something that the hedonist should encourage, unless that social control is based on sound moral principles (rather than capricious tradition). Especially ethnic cleavages and constraining gender roles is something that should be counteracted, for instance through education. Hedonist policies should give people the tools they need to seek out activities that fit their personality, but not if that leads to vain searches for an “identity”, or attempts to connect with one’s “heritage”, something which mostly serves to isolate groups and pit them against each other.
You can read more about what political applications I believe follow from hedonistic utilitarianism in my book Leftism (buy here).