That's likely to reduce diverse representation vs. single-member districts. If there are e.g. 8 seats a party could run 8 identical candidates and they'd all get the highest approval ratings for the combined district if one of them would, and other parties wouldn't get any.
List voting might work as an alternative to single member districts. You vote for your favorite party, and they are allocated a proportion of the total seats.
You lose the ability to know your local candidate, but how many people really do these days? It's what we set up in Iraq, but we don't do it ourselves.
It doesn't solve the problem that there is still exactly one chief executive. You can try making that a committee but that has other downsides.
> List voting might work as an alternative to single member districts.
But now you don't have a cardinal voting system and that's even worse than single member districts.
> It doesn't solve the problem that there is still exactly one chief executive. You can try making that a committee but that has other downsides.
Committees are dealing with it the wrong way. The right way to deal with it is to take away all of the executive's power. Constrain the national government from doing hardly anything and instead pass local laws to do whatever you want to do.
Then create elected positions responsible for different portions of the government. Directly elect the Attorney General and the heads of the major government departments. Let the President be like the Queen of England -- a figurehead with minimal responsibilities.
Germany has an interesting hybrid voting system that combines proportional representation via parties with local representatives.
In Germany, you cast two different votes. The first vote elects your local representatives via a first-past-the-post system; they all go to parliament. Then you fill up parliament with more people to make the proportions match those of the second votes cast all over the country. (There's lots of special cases and rules involved. Eg to handle the case when a party gets lots of first votes, but no second votes.)
