A Galilee primary? An Israeli White House nestled somewhere amid the hills of disputed Jerusalem?
Yet this week's national election here - at once exhausting, expensive, and inconclusive - has more than a few Israelis groping for a new way of deciding who will rule them.
At a time when issues like the badly ailing domestic economy and the future of the occupied West Bank seemed to call for strong government, Monday's voting produced instead a near-deadlock between Israel's ruling right-wing Likud bloc and the left-leaning Labor opposition.
As both major rivals try to piece together a majority in Israel's 120-seat Knesset, it is a host of much smaller, special-interest factions that holds the balance in the post-electoral bargaining.
''The lesson to be learned is that our system of voting does not work, it only produces stalemates,'' said an editorial writer in the Jerusalem Post. ''The time has come to make a change.''
Different people proffer different changes.
The most oft-heard suggestion is to reduce the input of fringe parties. This suggestion has gained wider currency by one particular new entry in that constellation, the vitriolicly anti-Arab Kach party of American-born Rabbi Meir Kahane.
This is the way Israel's system now works:
Each of the competing parties - 26 this time around - draws up a list of up to 120 prospective parliamentary candidates. Then the nation votes, each voter for the list of his choice. When all is tallied, parliamentary seats are dealt out proportionally on the basis of each party's nationwide vote total.
Labor, for instance, got about 35 percent of the vote this time. That means 44 or 45 seats, to be occupied by the top 44 or 45 names on Labor's candidate list. The exact figure will become clear only when full official results are released. But reports Thursday said that late-tallied returns from soldiers on duty in Lebanon had trimmed one seat from Labor's initial count of 45. The extra seat would go to the small, Likud-allied Tehiya party.
Rabbi Kahane's Kach party got one seat in the election, which will be occupied by Kahane himself.
Currently, to get even one seat a party must cross a ''threshold'' of 1 percent of the nationwide vote, or about 20,000.
The most commonly suggested reform in this area is to raise the threshold by at least a percentage point or two.
Other pundits, politicians, and professors argue that a more far-reaching change in the system is needed.
Some say greater power should be invested in the presidency, converting the post from its present, largely ceremonial status to something closer to the American model.
Others say Israel's more European-style parliamentary approach should be retained, but that the system of nationwide candidates' lists should be dumped in favor of party candidates' running for specific parliamentary seats in defined geographical constituencies.
Yet many reform advocates also suggest the current problems go well beyond the mere mechanics of voting and allocating parliamentary seats.
A virtually unanimous editorial chorus, for instance, lamented the midcampaign ''non-debate'' between Likud Prime Minister Yitzhak Shamir and Labor leader Shimon Peres.
Generally, both Likud and Labor managed almost perfectly to avoid overly clear-cut - much less, controversial - stands on major issues during the campaign. Similarly, there has been little major personnel change in the top leadership of either major party - with the exception of Mr. Shamir's assumption of the Likud mantle from retiring former Prime Minister Menachem Begin late last year. ''Ossification,'' the Jerusalem Post terms the problem.
In both personnel and policy, says one generally pro-Labor political analyst at Jerusalem's Hebrew University, ''It is time for both major parties to get rid of the deadwood; to raise the threshold for small parties; and generally to offer the country a real and identifiable choice.''
Still, there are more than a few local political experts who feel the post-electoral urge to reform the system may miss the point.
One candidate for the a small, Labor-allied party told the Monitor: ''You can't resolve social problems through technical means.''
He suggested that the election, mechanics aside, had accurately reflected a genuine national divide between two almost equally conservative and left-leaning camps.
He and many other Labor sympathizers say privately that they sense the national dynamic increasingly favors the conservatives - that, in any new election, Labor is perhaps likely to fare less well.
In any case, electoral reform could well prove easier talked about than carried out.
A change in the system would require parliamentary action. And, as one pro-Likud politican remarks:
''Unless both major parties carried exactly 50 percent of that battle, one or the other is apt to make political hay, try to take all the small parties and form its own government by the present rules of the game.''
Yet the problem of getting strong government remains. Prime Minister Shamir said, in an election-eve interview, ''The executive branch must be strengthened....
''A weak executive means a weak democracy.... As prime minister, I feel it keenly.''