OXFORD — When a Sunday school class needs to elect a treasurer, a name is put forward and everybody says “aye.”

That’s that. Nice and simple.

When Americans go to polling places, we often think electing a public official is almost as straightforward.

It’s not.

Take last week’s Republican Primary for U.S. Senate.

Had June 3 been a general election, the person with the most votes — Thad Cochran or Chris McDaniel — would have won, advancing to the November ballot.

But it wasn’t a general election and a third name was on the ballot. Because the tally between the incumbent member of the U.S. Senate and his challenger from the Mississippi Senate was so close, neither scored a majority (half of all votes cast plus one) and the resulting plurality means a runoff must be held June 24.

Now had the primary been in California or many other states, which use different rules, the names of all Senate candidates would have been on the primary ballot and the top two vote-getters (if their totals amounted to half the votes cast plus one) would advance to the general election — even if they were from the same political party.

Lots of states use that approach. It’s not better, just different.

And lots of general elections are won without any candidate achieving a majority.

President Obama polled majorities in 2008 and 2012 and George W. Bush did in 2004. But Bill Clinton served two terms in the White House without ever scoring more than half of all votes cast and in 2000 George W. Bush actually got fewer votes than Al Gore, but won on the electoral tally (which is a different animal altogether).

Mississippi has closed party primaries as far as the candidates are concerned, but open primaries as far as the voters are concerned.

That creates some interesting scenarios, too.

The potential for spoilers, for example.

A political party usually accepts the bona fides of any candidate wishing to seek a party nomination. In other words, the Mississippi Republican Party, a private organization, agreed Thad Cochran, Chris McDaniel and the third guy, Thomas L. Carey were “Republican enough” to be on the party ballot. But any Mississippi voter could vote in the party primary.

For example, former U.S. Rep. Travis Childers, who became the Democratic Party nominee for the Senate on June 3, could have voted for Cochran or McDaniel — whichever he thought would be easier to beat — if he had wanted to.

This situation — in which members of one party can team up and, in theory, pick the weaker of the other party’s candidates to advance to the general election — has been challenged in federal court. But it continues.

There’s no evidence this has ever been done on a large scale in Mississippi, but it has been done in other states with the same system and it has been done in local elections in Mississippi.

Strange situation. If Republicans have their nominee pretty much set (or even unopposed), they can turn out en masse to defeat the person they think is the strongest Democratic contender. And, when the shoe is on the other foot, Democrats can do the same.

Another wrinkle is that once qualifying ends for office, it ends.

Say Ernie Evil qualifies to run against Pete Popular and both win their party primaries. If something terrible — such as death — should befall Pete Popular between the primary election in June and the general election in November, too bad for Pete’s party. Qualifying does not reopen and the election proceeds. People might be stuck with Ernie Evil — a person not even a plurality of voters might enjoy seeing in office.

Turnout, by the way, was pretty good. Slightly more than 300,000 people voted in the Republican Primary, a record. Still, only half the people who voted Republican less than two years ago (711,000 Mississippians voted for Mitt Romney) cast a GOP ballot last week. Here’s a point: Every voter except those who voted Democrat on June 3 is eligible to vote June 24, including those who did not vote at all. It’s OK to participate in Round 2 even if you sat out Round 1.

Again, the point of all this is not to say Mississippi’s system is the best or the worst, could be or should be changed.

The point is merely to say that we may think of elections as pretty simple — name on ballot, people support you or they don’t. But there are rules and details that have the potential to change outcomes — even if they rarely do.

Charlie Mitchell is a Mississippi journalist. Write to him at Box 1, University, MS 38677, or e-mail cmitchell43@yahoo.com.