Social Voting with deeper gameplay?

Probably not exactly what your looking for. It has an interesting thinky part of how much help yourself and other players and a little bit timing/hand management. On your turn you get to the boss and make a deal for cash (a lump sum of cash comes from the bank). However, you need to bring other parties in on the deal. So you have some or a lot of the cash from the deal. Players can play cards to get them in on the deal, eliminate players from the deal or even become the boss. But the boss will be the ultimate judge of whether to make the deal.

https://boardgamegeek.com/boardgame/115/im-boss

I like this idea, but I think this is a very tough nut to crack.

The problem is that any sort of decisions based on subjectivity, (i.e. how much you like something, how funny something is, etc) can be influenced by any number of factors, including the status of the game, with no elegant ways to enforce the neutrality of the judgment. As you mention, you can just think, "Oh, Player A is winning so I won't pick their proposal" or "Player D is in last so I should pick theirs because they're not a threat to me anyway."

The one thing I could think of is that you could keep the proposals and the players that propose them to the judge separate somehow, where either a) you don't know how well each person is actually doing in the game or b) you don't know whose proposal is whose. A side effect of b) could be that the judge can try to infer whose proposal is the leading player's and avoid choosing theirs, but then this gives the leading player the incentive to provide proposals that seem like they'd be from other people. That system might work, with the right theme and system for making the proposals.

The other way to go about it would be the more Sheriff Of Nottingham route as mentioned:

Here, the judge's decision is based on their impression of how well each player is doing, which is relatively more objective. The choice you're given is "Who is doing the best, who should be punished?" as opposed a decision made on something separate than the status of the game.

TL;DR: Go in the direction of the judge not knowing who makes what proposal so the system can't be gamed, or make the decision based on the current status of the game, which is relatively less social.

P.S. I think a way of keeping the relative success of each player unknown would be the most creative way to go about this.

If you're going to go with the snake oil idea, then yeah, I think the best way to avoid gaming the system is to have the status towards the win condition uncertain or keep the reward of winning the pitch a little uncertain.

I think it could be really cool to have this idea and have the winnings be like, sets of resources or something, but you don't know who needs what resources or how badly. And you could have players choose between making a pitch and gaining some other sort of advantage. I think this could be a really neat niche between mindless party games and full-on strategy.

The Extraordinary Adventures of Baron Munchausen is an interesting case. In theory, I believe you should optimally use your tokens to introduce rather easy and boring uncertanties to the player who is most likely to vote for your own story in the end. That is, the system is gameable, but in a weird sort of social engineering way. I’ve yet to see anyone try to do that though. The basic framework can likely be adopted to include some more thinky elements with additional components, but I’m not entirely sure how and to what extent.

This superficially appears to be a solution very similar to Junta. That's a fun game too, but it's much more diplomatic than strategic.