Over the few games I've played, I've wished for upcoming agendas to be a bit more transparent, and for players to have more control over what is voted on.
I liked the idea of a pool/docket of agendas to draw from that everyone can see, and will probably try this out next time I play:
* at the start of the game, draw 5 agendas and place them face up (the docket)
* when agenda phase starts, instead of drawing an agenda from the deck, roll a 10-sided die to decide which of the face-up agendas is voted on first. If a face-down card is chosen, roll again
* after voting finishes, roll the die again to decide the next agenda and vote as normal
* after all voting is done, draw 2 new cards face-up from the deck and add to the docket
Politics strategy card:
For the relevant bit of the primary ability, instead: Draw 2 cards from the top of the agenda deck. You may discard a face-up agenda and replace it with one of these cards face-down. Place any remaining cards on the top or bottom of the deck in any order.
What this accomplishes:
* Players can plan better for agendas that may devastate them for the rest of the game
* Higher variance on the importance of Politics each round for each player
* Players holding Politics can use its ability as a bargaining tool
* Doesn't dramatically nerf/buff the speaker.
* Still lets the Politics holder strongly influence what is voted on during agenda phase without outright choosing.
If this makes Politics too strong, I'd think of casting simultaneous votes. Nice side effect of making agenda phase faster, and encouraging Politics holders to bargain with the speaker token.
If you want to do simultaneous votes give each player two card sleeves "First" and "Second" that read "For" and "Against" on different sides which can hold a reasonable number of planet cards. Let them state their position on each agenda but secretly load the sleeves with the planet cards they are voting for each agenda.
This makes zero influence planets useful for bluffing. You can stuff your zero influence planets in the sleeve corresponding to the agenda you don't care about.
When everyone has committed, count the votes for each agenda in order.
It should be possible to design the sleeves so they fold flat for storage. You could make six colored sets, or different sets for the sixteen council member factions.