Though national polls show that Democratic presidential candidate Michael S. Dukakis narrowly trails his Republican rival on the eve of tomorrow's general election, an overwhelming majority of Harvard students back the Massachusetts governor.

About 69 percent of undergraduates support Dukakis' presidential bid, compared to the 27 percent who back Vice President George Bush and 4 percent undecided, according to a poll of more than 300 students conducted by The Crimson November 3 to 6.

The Bush Campaign has pointed repeatedly to Dukakis' Harvard ties as evidence that the governor is so liberal as to be outside the American mainstream. The results of The Crimson poll seem to bear out this charge. Thirty-eight percent of Harvard undergraduates surveyed called them-selves liberals. About 44 percent of all students said they held moderate beliefs, and only 17 percent referred to themselves as conservatives, the poll showed.

The survey, a random telephone sampling of 311 undergraduates, is 95 percent likely to reflect accurately the opinions of the 6400-member student body within a 6 percent range of error.

The poll indicates a continuing trend of liberalism at the College. In 1984, 64 percent of undergraduates supported Democrat Walter F. Mondale over President Reagan. Mondale lost that campaign in a record-breaking electoral college landslide, as Reagan pocketed 49 states.

However, the poll suggested that freshmen do not grow significantly more liberal during their four years at Harvard. Slightly larger margins of freshmensupported both Dukakis and Bush than upperclassmendid, among whom undecidedvoters constituted a larger percentage.

Likewise, slightly more freshmen identifiedthemselves at both ends of the political spectrumthan upperclassmen, though the difference betweenfreshmen and upperclassmen at each end (1 percent)fell well within the survey's margin of error.

Houses also displayed a broad range ofpolitical opinion, though samples proved too smallto be sure that the results are accurate.

Bush carried only non-resident Dudley House, bya whopping 64 to 18 percent margin, with 18percent undecided. Meanwhile, Dukakis and Bushbattled to virtual ties in Eliot and KirklandHouses. Dukakis won most handily in Dunster andQuincy Houses by more than 5 to 1 margins, withthe other houses favoring the Democrat by about 3to 1.

Liberals outnumbered conservatives andmoderates combined in Currier and Dunster Houses,while conservatives showed most strongly inDudley. Moderates are in the majority at Cabot,Kirkland, Mather and Winthrop Houses.

Registered voters are also significantly morelikely to choose Dukakis than Bush, the surveyshowed. Among the 79 percent of the sample who areregistered, Dukakis led 72 percent to 25 percentfor Bush.

The notorious gender gap reproduced itself atHarvard. The Democratic combination of Dukakis andSen. Lloyd Bentsen (D-Tex.) won the allegiance of74 percent of Harvard women, with 23 percentfavoring Bush. Among men, Dukakis led 67 percentto 30.

Bush's selection of Sen. Dan Quayle (R-Ind.) asa running mate seems to have played itself out,with 57 percent of the students indicating thecontroversial selection of the young conservativedid not affect their choice. Four percent saidQuayle's place on the Republican ticket made themmore likely to vote for Bush, while 39 percentsaid the vice president's choice tipped themtoward Dukakis.

Among women, Quayle's significance to thecampaign declined. Two-thirds of the women polledsaid the selection of the handsome senator rumoredto have been chosen for his appeal to the oppositesex did not affect their choice. Among men, 51percent said Quayle did not matter. Women who wereinfluenced by Bush's choice swung almost entirelyto the Democrats, with only 2 percent sayingQuayle increased their support of the Republicanticket. Five percent of the men said Quayleboosted their support of Bush and 44 percent saidthe Indiana senator pushed them towards Dukakis.

House by House

The house by house percentage breakdown of thevote follows, with Dukakis' total listed first.

Adams: 73 to 27; Cabot: 75 to 17; Currier: 71to 18; Dudley: 18 to 64; Dunster 100 to 0; Eliot:47 to 47; Kirkland: 50 to 46; Leverett: 76 to 24;Lowell: 74 to 13; Mather: 69 to 25; North: 72 to28; Quincy: 85 to 15; Winthrop: 74 to 26.