Putting the Athenians aside, because their system is significantly different and different throughout the 500BC~338BC period as well, counting happens in parallel so there is no substantial difference between Australia's 24 million and India's 1.2 billion. The resources of the nation for counting, volunteers and money, scale with the population as well remember. The only difference is the final step, which is fairly trivial. Even if you had an election with a population equal to everyone on Earth it wouldn't be that different, there isn't any meaningful scaling problem.

I don't think there will be cost savings, and these machines will need to be replaced regularly as well so it won't be a one-off cost. And the present system isn't really expensive as elections aren't held every year, so that $600m price tag for the Indian election has to be weighed against the GDP of an entire electoral cycle of five years. We are talking about a price tag of around $120m a year for India then, against a GDP per annum of almost two trillion (if not higher, I am just going by 1.87 trillion for 2013). Per capita that's something like just under 10 cents a year from each Indian. I somehow doubt an IT project, which also has to accommodate all of India's many languages and scripts, is going to make a significant saving on that.

I am not aware of any research linking voting machines to turnout, have you got a source for that? I imagine some older people might even get frustrated and stay away. Australia has something like ~95% turnout through implementing a small fine for not voting (the tasty BBQs at many polling stations may also have an effect). There are also limited polling booths open before the election for those that expect to not be able to vote on the day.

So the benefits just aren't there, and as you say yourself "I don't know how we would implement such a system".

I wasn't really defending electronic voting machines. They're notoriously unreliable and as you point out are expensive and need replacement with time.

I was thinking something along the lines of voting online. There is significant research to support the idea that more people vote when it requires less time and effort to do so. Not just research, there are many political parties in America and elsewhere that try to improve their chances at the polls by making it more difficult to vote and keeping turnout low.

Voting online would improve the situation greatly, but it isn't easy to implement. To wit, the problems are

1. How to authenticate a user 2. How to map each voter to a vote, without keeping a record of whom he voted for 3. How to prevent fraudulent votes

I've thought about it but I couldn't come up with a good solutions to these.

Cost savings? Really? I don't know about other rich countries, but the country where I live spends about €1 per vote cast. All votes are counted twice, once on the night of the election and then a slow recount during office hours, both times manually, and it costs €1.

If there are many people to vote, there are many people to count. Summing up those votes is just on logarithmic order of complexity. Therefore sheer numbers are no argument.