There were some big winners in Utah’s primary elections Tuesday. But the biggest victory belongs to the primary elections themselves.

And the big loser — again, and deservedly so — was the caucus and convention system. A process that should finally be declared dead and given a decent burial.

Just the other day, the latest Salt Lake Tribune-Hinckley Institute of Politics poll showed voters favor, by some 2-1, a system that allows access to party primary elections by petition as well as through the caucus/convention system.

And Tuesday, rank-and-file voters, particularly among registered Republicans, were not shy about swatting aside candidates favored by the exclusionary caucus/convention system and choosing other, arguably much more moderate, people to stand for them in the November elections.

At the top of the ticket was Republican Senate hopeful Mitt Romney. The former presidential candidate, former Massachusetts governor and boss of the Salt Lake City Olympics easily won the nod with a good three-quarters of the votes cast.

That was a very different result than the outcome of the state Republican Convention back in April, when Romney came in a close second to Rep. Mike Kennedy, R-Alpine.

The same thing happened in the 3rd Congressional District GOP primary. There, short-term incumbent John Curtis thumped challenger Chris Herrod by a Romney-sized margin. Even though, in the convention, Curtis barely squeaked out a photo finish.

The argument in favor of the convention system is that delegates are less likely to be swayed by such things as name recognition or campaign spending. And a strong case could be made that, in the Senate and 3rd District races, that is just what happened.

But when a convention of basically self-selected true-believers tilts one way and the broad number of registered Republicans swings very much the other, anything resembling democracy should stand with the many over the few.

In both of Tuesday’s big contests, the eventual winner styled himself as a reasonable — conservative, but reasonable — representative of the people while their rivals claimed the mantle of the polarizer in chief who now occupies the White House. It is important, and reassuring, that those claiming to speak for the mainstream did so well and those hewing to an extremist position did so poorly.

That is, of course, the whole idea behind the move over the last couple of years to reduce the influence of the conventions, dominated by a few, and increase the importance of the primaries, where all those registered with the party have a say. Broadening the base, by its nature, tends to enlarge the tent and reward candidates who appeal to the sensible center.

Something all of American politics would benefit from.