(related to Problem: The Muddletown Election)
The numbers of votes polled respectively by the Liberal, the Conservative, the Independent, and the Socialist were $1,553,$ $1,535,$ $1,407,$ and $978$ All that was necessary was to add the sum of the three majorities ($739$) to the total poll of $5,473$ (making $6,212$) and divide by $4,$ which gives us $1,553$ as the poll of the Liberal. Then the polls of the other three candidates can, of course, be found by deducting the successive majorities from the last-mentioned number.
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