Just like spinoff of companies or stock dividend payout, value shall not be created from thin air. If a stock before dividend payout is at price 10.0 and the dividend is 1.1 then the stock price after dividend payout shall be 8.9 by arbitrage-free condition. There is no airdrop ever.
Same rule applies to chain split. Assume, for example, bitcoin is priced at P before the split and there are three chains after the split. Let P1, P2, P3 be the prices of coins (aka UTXO) only valid in chain1, chain2, chain3. Then it must be P = P1 + P2 + P3. Prices of any coin can be calculated accordingly. For example, by tricks to split the coins and arbitrage-free condition, a coin only valid in chain1 and chain2 must be priced at P1 + P2; craft a transaction with an input coin valid in all chains and one new mined coin of chain3, the input coin is now only valid in chain1 and chain2 because this transaction is invalid in chain1 and chain2 and therefore not consumed in chain1 and chain2 ever. An important fact is that, after the chain split, any two coins recorded in the same chain, being valid in this chain, may possibly have different price because one coin can/will be consumed and recorded in chain2 while the other coin was destroyed in chain2 already. There shall be markets for coins of different groups so a market signal can guide people how to best use these coins. There shall be features for wallets so a consumer can easily pick the coins of a specific group.
The price is proportional to mining energy power in a proof-of-work system. While the three factions agree to disagree or even never talk to each other in a round table, they can simply fork the chain and commit their mining power to their chain. Before the chain split, all the three factions mine on the same chain with total energy power P. After the chain split, each faction commits Pi energy power and P = P1 + P2 + P3. While people jump from one ship to another, sometime P2 > P3 therefore coin only valid in chain2 is higher price than coin only valid in chain3, some other time P2 < P3 therefore coin only valid in chain2 is lower price than coin only valid in chain3. However, the price of coins valid in all chains, aka the price of the coin before chain split, remains. As times goes by, maybe chain1 dies, then chain1's price and energy power P1 moves into chain2 and chain3. Because a zero-price coin has no economic impact, chain1 is omitted. Coins valid in all chain must be coins valid in chain2 and chain3 as well and in addition coins only valid in chain2 and chain3 becomes part of the coins valid in all chains.
So, which coin shall be named bitcoin? With pricing continuity at the split and highest price and stability under the condition of replay benefit, it shall be coins valid in all alive chains. And its coins will evolve and never die.
If Joe understands all above, he may wonder what a nonsense to go for a war while it is all possible to evolve the bitcoin rules in a permission less way and allows multiple chains to flourish by the same network effect; everybody might have already the coin ready for an innovative idea of a crazy guy without notice until the chain is pricy enough and surfaces to the exchange being part of "all alive chains".
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