Nowadays, it seems to be taken for granted that parliamentary deputies are elected from geographic constituencies. This can take the form of single-member districts, as in the US, Canada, and Great Britain, or of multimember districts (especially in countries with proportional representation). But there are several alternative possibilities:
(1) On the crudest level, people could be represented in alphabetical order. People with names from A to Ag would vote for one Representative, those from Ah to Ay for another, and so forth. This would avoid any danger that a Representative would not pay attention to all areas of the country; yet it would leave him or her with a manageable number of constituents, not too many to deal with. (True, it might be hard to meet all the constituents physically, but the Wonders of Modern Communication, above all the Internet, will take care of that.)
(2) People might be represented by the economic groups they belong to--a certain number of Representatives for steelworkers, cattle ranchers, merchants, etc. This has gotten a bad name because of its association with the Fascist "corporate state" (and it was also tried by at least one Communist country--Yugoslavia for a while had a "Producers' Council"
https://en.wikipedia.org/wiki/Parliament_of_Yugoslavia) but I don't see why in principle it's not compatible with democracy.
(3) In multinational states, people might vote by their nationality. The difference between this and various federal systems where the geographical units are organized according to nationality is that groups who do not constitute a majority in any particular region would be assured of representation. (This idea occurred to me when reading about the Bauer-Renner idea of "extraterritorial autonomy" for the minorities of Austria-Hungary and the Jewish Workers' Bund's proposals for Jewish autonomy in Tsarist Russia.
https://en.wikipedia.org/wiki/National_personal_autonomy)
(4) Representatives might be elected by age groups. Of course a Representative need not be the same age as the group represented, but there would be a tendency for representatives of younger age brackets to be younger, etc.--or would there be, given for example the 74-year-old Bernie Sanders' appeal to young voters?
(5) Or there could be representation by gender. This is not quite the same thing as the proposals made in some countries to have minumum quotas of women in Parliaments. It is simply a proposal to have all-male and all-female *electorates* The women could elect a man, or vice versa.
Most of these proposals could of course be attacked as "divisive." Yet why is dividing people by, for example, age more harmful than by geographical area? Different geographical areas have, after all, gone to war with each other, which has not happened with age groups or sexes. (And tension between economic interests within a nation rarely results in outright war, either--"class war" is *mostly* a metaphor.)
Can anyone think of some other possibilities?