Its really sad to see how a technical question gets disappeared with 0 replies in this spam board. Hope theymos implements Altcoin Technical Discussion board soon.
Coming to your question
A cryptocurrency uses a certain algorithm because it needs to serve a particular purpose. The cryptocurrency can divided into various types based on the purpose of its creation. For example Btc uses Sha-256, Eth uses Dagger-Hashimoto algorithm, Ripple uses ECDSA, Litecoin uses Scrypt, Dash uses X11, Monero uses Cryptonight and so on.
Let's consider Btc. It was created by satoshi for the purpose of using it as digital equivalent for currency. Hence in order to have higher security, shorter btc addresses and to mine currencies using POW Sha-256 was used.
Why does Eth use Dagger-Hashimoto?
A quote from github documentation of Dagger-Hashimoto will help you out.
Dagger-Hashimoto advantages :
ASIC-resistance: the benefit from creating specialized hardware for the algorithm should be as small as possible, ideally to the point that even in an economy where ASICs have been developed the speedup is sufficiently small that it is still marginally profitable for users on ordinary computers to mine with spare CPU power.
Light client verifiability: a block should be relatively efficiently verifiable by a light client.
With an additional modification, we also specify how to fulfill a third goal if desired, but at the cost of additional complexity:
Full chain storage: mining should require storage of the complete blockchain state (due to the irregular structure of the Ethereum state trie, we anticipate that some pruning will be possible, particularly of some often-used contracts, but we want to minimize this).
Similarly Dash uses X11 in order to improve the safety of its currency. Dash or any other currency using X11 algorithm will be unsecure only when the 11 hashes were broken at the same time.
what makes the developers of a coin decide upon a particular algorithm for the protocol to operate with?
They decide in order to make their currency more secure and to fulfill the coin's purpose of creation.
