Wouldn't rolling a dice be a better way to fix the honour bid.
1. All players make their bid from 1 to 5
2. One 0 to 5 dice is rolled (you can get them pretty easily) https://www.tarquingroup.com/dice-games/specialty-dice/black-and-red-dice-0-5-set-of-50.html
3. All player compare their bid to the roll. They then lose or gain honour to the honour token pool not between each other.
4. Players draw the number of cards equal to their bid.
Let's run a quick example.
3 players bid, player one bids 1, player two bids 3 and player three bids 5
The dice roll is a 3
Player one. Draw 1 cards and receives 2 honor
Player two draws 3 cards and doesn't lose or receive any honour
Player three draws 5 cards and loses 2 honour back to the token pool.
I like this idea better than the restrictions placed on bidding in the rules.
I think this would work as all players are against the single roll. The only difference would be when the dice rolls 0 and would drain some honour from every player or you could say that if the dice rolls a zero that mean all playera lose zero honor, that would work quite nicely too.
Edited by Maffster