A better model for a shotgun clause is one in which each partner names the price they would pay for the company. The partner who names the higher price then buys the company at the price half way between the two prices. Both partners win. The buyer gets the company at a discount to what they were prepared to pay, while the seller gets a premium to what the company was worth to them.
To fix this, you need to have both parties commit to their prices before anyone learns anyone else's price. For example, you could require both parties to mail their offers to the company lawyer, who is only allowed to reveal them when both offers have arrived.
Of course, with the above solution, you have to trust a human being (the lawyer) to be impartial and not collude with one of the cofounders against the other. For the paranoid, you can instead use a protocol that trusts cryptography instead of humans. You could have each person choose a random nonce, publish H(price + "#" + nonce). When everybody's published a hash, everyone then reveals their price and their nonce -- you know the price was chosen without knowledge of the other party's offer. (Of course each person needs a public key to sign the hash as well, to make sure a participant can't legitimately claim "I didn't send that.")
That's a nice twist. I used 'person that quotes highest buys out the other parties at that price', but yours is even better I think. Thanks!
The parent way can be gamed: the loser may benefit from deliberately bidding a bit higher than they would otherwise to force the winner to pay more.
(Although you can argue this both ways, and auction theory does, I feel like this quirk could create animosity)
When I started a company long ago, a consulting partnership, my cofounder and I picked the simplest dispute resolution mechanism: if we really couldn't agree on something, one person could name a price and the other could decide to buy or sell at that price, giving the purchaser sole control. It's basically the equivalent of how you teach two kids to cut cake in half.
I was skeptical that we even needed that; after all, it was a partnership. With a friend! What could go wrong? But our lawyer insisted.
Turned out he was right. I learned two lessons: 1) get a good lawyer at the start, and 2) it's worth thinking through the common bad outcomes and agreeing on how to handle them before the bad situation hits. Because once you're in a dispute, it is way too late to try to get agreement on how to resolve disputes.