The US has a federal system of government, with power shared between the 50 states, one district and several territories. Every 4 years an election is held to select a President and every 2 years an election is held to select members of the House of Representatives, and every six years, elections are held to select members of the Senate. So, at the 2012 election, and the 2016 election, people voted for the President, all members of the House of Representatives, and 34 members of the Senate.
Like the US, Canada and Australia both have a federal system of government, with Canada having 10 provinces and 3 territories, and Australia having 6 states and 8 inhabited territories.
Canada has federal elections for the lower house, the House of Commons, every 5 years, while members of the Senate are appointed by the Governor General, on the advice of the Prime Minister.
Australia has a federal election every 3 years at which all members of the lower house, the House of Representatives are elected, and half the members of the upper house, the Senate, are elected. Senators are elected for 6 years.
The most recent Canadian Federal Election cost the nation $443 million in total. This includes the cost of running the election as well as campaigning for that election. In Canada, voting is not compulsory, so 68.5% of eligible voters turned out to vote. This was 17,546,697 of those eligible. Therefore the cost of the Canadian election was approximately $C25.25 (~$US19) per ballot cast.
The 2013 Australian federal election (the last for which figures are available) cost $193,774,374 to run. In addition, the two major parties spent approximately $30,000,000 on their campaigns. So, the election cost around $224 million in total (running of election plus campaign costs). In Australia, voting is compulsory, and in the 2013 election 12,914,927 ballots were cast. So, the cost of the election comes to about $A17.34 (~$US13) per ballot cast.
The 2012 US election campaign alone cost an estimated $US6.3 billion. It has been estimated that the cost of running the election itself was over $US1 billion. So, a federal election in the US costs about $7.5 billion and given that just under 129 million ballots were cast, that comes to about $US58.14 per ballot cast. That makes the US election about 4.5 times as costly as an Australian election per ballot cast, and about 3.1 times as costly as a Canadian election per ballot cast. The high multiple for Australian elections is due to voting being compulsory. However, if it is assumed that the same proportion of Australians would vote as Canadians did (68.5%) in their 2015 election, then the US election is still 3.0 times as costly to run on a per ballot cast basis.
$58 per ballot cast is ridiculously expensive. If US elections operated at the same rate of per vote expenditure as Australia, then every presidential cycle they would have almost an extra $US6 billion to spend on schools, hospitals, and other useful things.
Sources
http://www.cbc.ca/news/politics/elections-canada-443-million-1.3436139
https://en.wikipedia.org/wiki/Federal_political_financing_in_Canada
http://www.elections.ca/content.aspx?section=res&dir=ces&document=part6&lang=e
http://time.com/money/4556642/election-day-2016-costs-country-voters/
http://www.aec.gov.au/Elections/Australian_Electoral_History/Cost_of_Election_1901_Present.htm
