>1. by random selection, every social category is represented equally
No, every social category would be represented similar to their ratio in the rest of society. This wouldn't line up well with many groups that want much stronger support for minorities.
Take Native American concerns for example. With just over 1% of the population being Native American they will probably only end up with a few representatives out of the 100. The remaining ~98 people are going to be spending a bunch of time concerned about their own problems and won't put effort into making sure Native Americans get equitable treatment due to past issues.
In other words, by cutting out the ability to lobby for rich people to help themselves, you also cut out the ability to lobby for legitimate issues as well. Lobbying has (rightfully) been seen as a terrible thing, but it does have the legitimate purpose of bringing issues to a representative's attention that he/she would never even think about otherwise.
There's also the point that 100 random people won't have any background on the topic in question. Who's going to help them understand it? Most likely the same vested interests that today lobby the government.
It's a fun solution to consider, but I'm also concerned in that lobbying for this solution already exists - mass marketing, which has already been mastered.
My parents had me at 17 and had no idea how to raise kids. They see a commercial of kids eating cereal and poptarts, so they feed me cereal and poptarts under the false assumption that that is a healthy meal, and that plus other factors led to me growing up fat and unhealthy.
Basically, if lobbying is a problem, disinformation through mass marketing is a MAJOR problem.
No, every social category would be represented similar to their ratio in the rest of society. This wouldn't line up well with many groups that want much stronger support for minorities.
Take Native American concerns for example. With just over 1% of the population being Native American they will probably only end up with a few representatives out of the 100. The remaining ~98 people are going to be spending a bunch of time concerned about their own problems and won't put effort into making sure Native Americans get equitable treatment due to past issues.
In other words, by cutting out the ability to lobby for rich people to help themselves, you also cut out the ability to lobby for legitimate issues as well. Lobbying has (rightfully) been seen as a terrible thing, but it does have the legitimate purpose of bringing issues to a representative's attention that he/she would never even think about otherwise.