John Rawls’ A Theory of Justice famously introduced the idea of an “original position,” a hypothetical situation in which citizens would come together behind a “veil of ignorance” to select principles of justice that can regulate their common life. There are different ways of understanding the OP, but one useful way — which Rawls himself favoured later in life — is to imagine that the “contracting parties” in the original position are not the members of society themselves, but rather their representatives. Each of these representatives — modelled as rational negotiators — is then supposed to bargain for the best possible “deal” acceptable to the citizens they represent on the terms of cooperation in society, but without knowing which specific set of citizens they represent. This is supposed to ensure that the negotiating parties will only agree on principles that would be acceptable to all citizens as “free and equal.”
There being no real-life analogue for such scenarios, please allow me to oversimplify by offering a scene from family life. Two children argue over who gets how much pie. Parental unit decrees that Child 1 gets the piece he desires — but that Child 2 will actually cut the pie. The Rawlsian legislator is never quite sure whether he is Child 1 or Child 2, and therefore he has to make his decision, not on behalf of a narrow constituency, but with the interests of all pie consumers in mind.
Implementing such a legislature, of course, is easier said than done:
An example [from New Zealand] may help. Imagine the electors for Wellington Central elect Grant Robertson their MP. At the end of his term, the Electoral Commission randomly assigns him a different constituency. Say he draws Auckland Central, for example. Robertson then has to go to Auckland Central to defend his record in parliament; let’s say he’s given one month to make his case. Auckland Central then holds an “up or down” vote deciding whether or not he can run in the next election. If he’s voted down, he cannot run in that electoral period (though he may run in later periods — no permanent disqualification is envisioned here); otherwise, he gets to run again, if he so wishes, in Wellington Central.
At no time does Mr Robertson’s official constituency change; however, whenever standing for election, he must make his case, not only to them, but to an entirely different district as well.
I don’t envision this happening in the States anytime soon — it would require substantial changes to the Constitution, and apparently no one currently holding national office has so much as read the Constitution — but it’s something to ponder while the politicians pander.