I would prefer if the input to the software was published and anyone could verify the outcome. Unfortunately, currently none of this information is published and the whole system is based on trust.
Having audited the source code really doesn't help; it won't remove the need to perform independent verification.
Similarly, merely publishing the input won't help much either; how do you verify that the published input corresponds to the actual votes? It won't remove the need for independent parties to observe the raw input (paper votes) and to make their own tallies; in which case those parties can publish their own copies.
Asking for the input to be published and the source to be published is just scraping the surface and won't add meaningful security. You need independent observation by mutually distrusting parties.
Personally I understand your point, but I think auditing the code is a good and important first step.
Technically it's worth noting that a code audit is required in any "perfect solution", so it isn't wasted effort.
Politically it is important to establish the principle that the AEC should be required to respond to reasonable requests to verify how the process is implemented.
Similarly, merely publishing the input won't help much either; how do you verify that the published input corresponds to the actual votes? It won't remove the need for independent parties to observe the raw input (paper votes) and to make their own tallies; in which case those parties can publish their own copies.
Note that in Australia vote counting itself is manual and is already observed by multiple hostile parties. No one is proposing removing that.
Let's say that the software is published, and the code is audited and it looks ok - it seems to implement all of the intricacies of the transfer system and so on correctly. Then what? What if the operator forgets to use the latest version? or puts a different piece of software entirely on the counting system?
Since we already have access to the raw counts the audited code can be run by anyone to verify it outputs the same output as the AEC claims.
[1] http://results.aec.gov.au/17496/Website/SenateResultsMenu-17...
[2] http://results.aec.gov.au/17496/Website/External/SenateState...
However in extremely close races, such as what happened in WA - it can come down to very small numbers of individual ballots and how their preferences are stated, as to what order senators are elected in.
This then affects the re-flow of preferences.
The best you could do is compare the expected flow each step, based on group voting ticket, against the actual flow, and make sure the total difference does not exceed the number of below the line votes.
Edit: Antony green has an estimate used in his calculator. "At Federal election, around 95% of mainland voters, and 80% of Tasmanian voters, fill in their ballot paper using the group ticket ('above the line') voting option."
http://www.abc.net.au/elections/federal/2007/calculator/sena...
With the number of candidates doubling last election, Tasmania was probably more like 90%.
http://blogs.abc.net.au/antonygreen/2013/08/record-number-of...