Hare was said to have been 'conspicuous for great industry – to have wide interests in life and clearness of intellectual vision'. He was a member of the London-based Political Economy Club and the British Dictionary of National Biography says of him:
Hare's energies were concentrated in an attempt to devise a system which would secure proportional representation of all classes in the United Kingdom, including minorities in the House of Commons and other electoral assemblies.
His original electoral system ideas included making England one huge constituency (later he changed this to seven or eight hundred constituencies) and that each voter would sign and check his vote. By 1873, however, he had adapted his ideas to take account of the secret ballot. Under Hare's method, simply dividing the vote by the number of seats constituted the quota, and then the surplus was expected to be distributed 'at random'.
Hare's famous original work Machinery of Representation appeared in 1857 (in two editions) and many editions of his equally famous Treatise on the Election of Representatives: Parliamentary and Municipal appeared between 1859 and 1873. In the preface to the fourth edition he stated his belief that proportional representation would '... end the evils of corruption, violent discontent and restricted power of selection or voter choice'. A great deal of writing on this theory developed and several societies were formed worldwide for its adoption, although Hare pointed out that his scheme was not meant to bear the title 'representation for minorities'. Moreover, he noted in the preface to his third edition a point that was to become a feature of Tasmanian politics:
Can it be supposed that the moment the electors are allowed a freedom of choice they will immediately be seized with a desire to vote for some distant candidate with whom they are unacquainted, rather than for those whom they know – who are near to them, whose speeches they have heard and who have personal recommendations to the favour and respect of the town and neighbourhood.
Finally, with the help of contemporaries such as John Stuart Mill and Catherine Helen Spence, Hare popularised the idea of proportional representation worldwide. The permanent recognition of his name in the Tasmanian system is perhaps appropriate despite little being left of his original proposals. His death in May 1891 occurred several years before the first use of proportional representation in Tasmania in 1897.
The former London headquarters of the Electoral Reform Society was named in his honour.