It is ironic that, in the city that produced Abscam and Watergate, some citizens should suddenly worry that Washington is about to be invaded by "dirty-money types."

But this has become a major issue in the referendum on legalized gambling that voters in the District will decide today. Many people who have no moral objections to gambling wonder whether dog racing and jai alai will attract undesirables or otherwise alter the character of our city for the worse.

The question is a legitimate one, but most of the answers to it have been emotional rather than rational. In the past two days, a couple of revealing arguments on the subject appeared on The Washington Post's editorial pages.

Both Bill Raspberry and Juan Williams wrote about the illegal numbers game that flourishes in Washington, and both wrote about it with sympathy. Williams described his mother's passion for the game and her regular dealings with the numbers man who (in the eyes of the law, if not mother) is a criminal.

Neither columinst found anything particularly reprehensible about this form of gambling. I can find plenty of things wrong with it: the numbers game is an outrageous rip-off of the people who play it; it is antirational; profits from it wind up in the hands of undersirable elements of society.

Yet while both columnists defended numbers, they opposed the legalization in the District both dog racing and jai alai, games that would be regulated by the government and whose revenues would benefit the city as a whole.

This position is inconsistent but understandable. People who have grown up around the numbers game know that it is hardly as sinister as moralists and legalists would suggest. (Not many babies are going without milk because mommy plays the numbers. The numbers man is more apt to be a friendly neighbor than an underworld heavy.) But these same people may fear pari-mutuel gambling because it is unfamiliar to them.

Raspberry wrote: "Maybe there is some reason to suppose that dog tracks and jai alai would attract to Washington some people we'd just as soon not have as neighbors: organized-crime figures, fixers and other dirty-money types . . . The question, really, is whether the gains in revenue, employment and entertainment are worth the risks involved in bringing alien games to the District."

They may be alien to Raspberry, but they are not alien to me. I have been to jai alai frontons from Miami to Macao, dog tracks from Denver to London, and the fear that these games can adversely alter the character of a city is not supported by reality anywhere.

When people think of legalized gambling, they think immediately of Las Vegas, whose culture and economy revolve around gambling, and whose ethos I don't think any city should want to emulate. But the existence of a race track does not turn a city into a Vegas.

No city in the United States is more pari-mutuel crazy than Miami. The greater Miami area has three thoroughbred tracks, two jai alai frontons, four dog tracks and a harness track.

And yet these gambling emporiums hav not significantly affected the character of the city. A tourist or a native can live his life there oblivious to their existence.

Miamians who don't gamble aren't bothered by these pari-mutuel establishments (except, perhaps, for an occasional traffic jam). Those who do gamble have wonderful opportunities for diversion. This is true in every major city that has legalized gambling.

Boston is a big dog-racing town but the sport hardly has altered the special character of that city. Nor has the Mile High Kennel Club spoiled the purity of the Rockies for John Denver.

And even though any gambling game is going to attract some people looking for a quick, dishonest buck, pari-mutuel betting hardly serves as a magnet for armies of "dirty-money types." All things considered, I would feel more confident in the integrity of a Washington dog track than that of the Congress.