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I'm watching this Lightning Network presentation by the original authors. At 9 minutes in, he notes that all the network sees will be a transaction to the multisig address and then a transaction to Alice for 0.8 BTC and a transaction to Bob for 0.2 BTC.
Is all of this effectively 3 transactions? Would it not be cheaper and clog the blockchain less by simpling having Alice send 0.1 BTC to Bob and then another 0.1 BTC to Bob and have 2 transactions instead of 3?
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Is all of this effectively 3 transactions?
No, assuming you mean '3 on-chain transactions'. It is useful to make a distinction between an 'on-chain transaction' and a payment being sent. To open a LN channel requires one (on-chain) transaction, and to close it requires another.
But while the LN channel is open, the participants can send each-other an unlimited number of payments using the channel (up to their channel capacity, of course). These payments are not recorded on-chain, instead their LN nods keep track of the channel's current state. This allows for more efficient use of blockchain space, while simultaneously giving the channel participants a mechanism for sending payments efficiently and without needing to trust their counter-party, or a third party.
Further, the channel participants can also route payments to other LN users, assuming that there is a valid route with the proper capacity available. A highly connected LN graph could allow all users to make payments to each other, without needing to constantly publish on-chain transactions.
