A Chicago woman told academic researchers in 1960 why she decided to vote for John F. Kennedy after his first debate with Richard Nixon.

"It was Nixon's eyes," she said.

"What about his eyes?" the professors asked.

"Well," she replied, "it was the left one. It looked shifty."

Election analysts are often reduced to evidence of this sort to explain the "psychodynamics" of the American voter. The presidential election of 1984 is no exception. Things happened that, on the face of it, make little sense.

There is among the electorate, for example, a small group of people -- about 8 percent -- who describe themselves as "very liberal." They would be, in the common jargon, "left wingers" not much in tune with President Reagan and his policies. Yet, about 40 percent of them voted for Reagan, according to exit polls conducted by NBC News. Was it Walter F. Mondale's eyes?

The demographic reports from Tuesday's election are full of similar anomalies. The Republicans are called the party of the rich, the Democrats the party of the poor. But 40 percent of the poorest people voted for Reagan and a third of the richest people voted for Mondale.

Within the precincts of the Sierra Club and other environmental lobbies, Reagan is one of the leading figures on any enemies list, just behind his former Interior secretary, James G. Watt. ABC News set out to track the voting behavior of "strong environmentalists" on Tuesday and discovered that 40 percent of them cast ballots for Reagan.

Then there was the anti-"big spender" bloc that cast one-fourth of its votes against Reagan and a pro-Equal Rights Amendment bloc that cast one-fourth of its votes against Mondale.

The lesson is perhaps one that most politicians have learned -- voters can be ornery. In Tennessee yesterday they returned a prison convict to the state legislature, and in Idaho they may have reelected Republican Rep. George Hansen, who is under a federal prison sentence.

Theorists of a somewhat different bent can make a respectable argument that most voting behavior can be explained in terms of self-interest.

Thus a left-wing ideologue can give his vote to Reagan because he is prospering and doesn't want higher taxes.

A right-winger can -- as 15 percent of them did -- vote for Mondale to protect his unemployment or Social Security check.

There is considerable evidence in the exit polls to support the "self-interest" theory.

Among voters who said they have been "better off" under the present administration, 86 percent voted for Reagan. Among those who said they were "worse off," 84 percent voted for Mondale. Among those who expected their family financial fortunes to improve in the coming year, 76 percent voted for Reagan. Of those who expected financial setbacks in the next year, 84 percent chose Mondale. And while there were defections from both groups, the richest voters gave Reagan a large majority and the poorest voters gave Mondale a large majority.

Another theory involves single-issue and special-interest voters. The evidence here is mixed and often contradictory, according to Tuesday's exit polls. The AFL-CIO, as a case in point, invested millions of dollars and countless man hours on behalf of Mondale. But only 6 percent of the voters said labor union endorsements had influenced them. Their votes were evenly divided between the two candidates.

The abortion question pitted a loud antiabortion lobby against an equally vociferous pro-choice lobby. Only 15 percent of the voters said the candidates' stand on abortion was significant; 63 percent of this group voted for Reagan, 37 percent for Mondale.

Sixteen percent of the electorate said the nuclear freeze issue motivated their choice for president; 64 percent voted for Mondale, 36 percent for Reagan.

There are several difficulties in slicing up the electorate into single-issue cohorts and thereby measuring the power of the lobbies.

The first problem is that single-issue voters usually turn out to be voters who, in their personal catechisms, attach "great importance" to a variety of issues.

Thus, the antiabortion or pro-abortion voter may fairly be claimed as an apostle by several "single-issue" groups.

The larger problem is that the theory is often refuted by historical experience. That seems to have happened this year in the voting behavior of women.

It was argued by some Democrats and feminist organizations, for example, that a woman vice-presidential candidate would lock up the women's vote for Mondale. But a sizable majority of women voted for Reagan, and the exit polls claimed that Geraldine A. Ferraro's presence on the Democratic ticket cost the party more votes among women than it gained.

Political analyst Horace Busby, who forecast long in advance the electoral outcome of the 1980 and 1984 presidential elections, rejects the notion that "shifty" eyes or single issues or even self-interest are the prime engines of voting behavior in the United States. His is the idealistic view that the American electorate is more wise than dumb, more unselfish and motivated more by a sense of the national interest than by personal interest or circumstance.

The people know what is happening in the country, he says, because of America's remarkable communication system, and they are able to see themselves in a national context and weigh their political decisions in that context.

When they say they are "better off" today and vote for Reagan they are not merely expressing a selfish interest, Busby contends.

Rather, he argues, they are saying that this is the kind of society and these are the kind of times they want for the whole country, not for themselves alone.

In this sense, he sees the American voter as a citizen philosopher who has given another landslide to a president who is "a common man, the sort of person the ordinary guy could sit and talk with and be understood."

Busby enjoys needling the "Washington elite" who consider Reagan "dumb" and conclude that the voters are "dumb."

"They're not dumb," he says. "They know the kind of country they want, and it's the kind of country the Republican presidential party understands. Liberal Democrats always blame their defeats on the popularity of the victor. They don't understand that it's the message and not the messenger that defeats them."

That is classical, old-fashioned political theory, and there is nothing in the exit polls to validate or refute it. There is something in the polls, however, about who is and isn't "dumb."

Voters leaving some polling places on Tuesday were asked if it was important for a president to know a lot of things about his job and how to handle it. They replied affirmatively and on that score gave the laurel to Reagan. But only by 4 percentage points.