Rattlesnakers are more numerous than Republicans in Nevada, where Democrats boast their greatest registration and legislative majorities in the intermountain West.

Nevertheless, Republican Attorney General Robert List has established himself as a solid favorite to defeat Democratic Lt. Gov. Bob Rose in this year's gubernatorial election.

List's position reflects his popularity, Nevada's traditional conservatism and lingering doubts about whether Rose would be vigorous enough in enforcing strict laws designed to keep the underworld away from the state's legal gambling industry.

Despite a nearly 2-to-1 Democratic registration advantage and a 52-to-8 Democratic edge in the legislature, List's chances are so bright that the state has been targeted by the Republican National Committee as one of the best prospects in the West.

Every western state except Alaska now has a Democratic governor, but the GOP hopes to change that this year in Nevada, Oregon, Colorado and Wyoming. Of these four, only Nevada is without a Democratic governor seeking reelection.

List who needs an estimated 35 percent of the Democratic vote to win, has campaigned for a state spending limit that would be tied to population growth and inflation. Rose, who calls this approach "wishful thinking," has countered with a plan for a 30 percent across-the-board cut in property taxes.

Nevada is a right-to-work state, and Rose may have been damaged in the primary by a disclosure by United Press International reporter Cy Ryan that Rose had passed along a message from a Culinary Union official at Harrah's Club in Reno asking whether the big hotel-casino would be receptive to union organizing.

Most northern Nevada casinos, unlike their Las Vegas counterparts, are nonunion and want to stay that way. Rose's opponents in the primary accused him of being "an errand boy" for the Culinary Union, a label that has picked up by List.

Both the 42-year-old List and the 39-year-old Rose are former district attorneys. They have matched their crime-fighting records in a way that sometimes suggests they are running for sheriff instead of governor.

Rose, however, goes further. He calls for a ban on all plea bargaining, as a means of ensuring that criminals receive longer sentences. List says that proposal is "a cruel joke" and contends that some plea bargining is necessary for the orderly functioning of the criminal justice system.

Both candidates have shown themselves capable of political blunders. Even some Republican officials say privately that List overreached himself on primary night when he launched into an uncharacteristic ideological attaack on Rose.

"This is the first time in Nevada history that the Democratic nominee for governor is an Eastern-style, left-wing liberal," List said. "Rose is out of step with his party and out of step with Nevadans."

Rose responded with a series of radio commercials denouncing List's "smear," which he took a reflection on his native state, New Jersey. List said the accusation of liberalism was based on Rose's serving as a messenger for the Culinary Union, which he claimed was "typical of Eastern labor pracatices."

But Rose's political mistake probably has been the more serious one. In the primary he made a number of Nevadans uncomfortable when he advocated that the state go easy in enforcing its "foreign gaming" law, which gives the Nevada Gaming Commission the power to prevent casinos from setting up branch offices in other states that legalize gambling.

The theory behind this law, which List as attorney general argued successfully all the way to the Supreme Court, is that Nevada must have control of gambling licenses even when they go beyond state borders in order to prevent criminal elements from gaining influence.

Many Nevadans who have nothing directly to do with gambling have a dual attitude toward the state's No. 1 industry. While they accept gambling as necessary or even beneficial because of the public and private revenue it generates, they are worried that the immense profits invariably will attract orgganized crime.

That worry increases at election time, becuas casinos are the chief political contributors. The current governor's race will cost each candidate an estimated $700,000, with most of the money coming from casinos and hotels.

The casinos contribute because the governor appoints the gaming commission. Though the commission has been untouched by scandal, it always is considered a potential target for the underworld.

This year the uneasiness is greater than usual, partly because of reported improprieties involving New Jersey and partly because Florida will vote on legalizing casino gambling.

List, who thinks that New jersey laws may be too weak to keep out the underworld, says that Nevada's gambling industry ultimately will be jeopardized by federal intervention unless the foreign gambling law is strictly enforced.

Rose has backed away from his earlier criticism of the law, but he has been hurt by his original stand.He has been endorsed by his leading primary opponent, Las Vegas attorney John Foley, who made the gambling issue a principal one in his campaign.

Nor, in all likelihood, does Rose have the backing he needs from retiring Gov. Mike O'Callaghan, who is so popular that Democrats and Republicans alike say he could be reelected almost by acclamation.

O'Callaghan, who likes List and has worked with him for eight years, is scheduled to endorse the entire Democratic ticket later this month and make a token appearance in Rose's behalf. But it is widely believed in nevada that a List victory would not disappoint the governor.