You don't need a public record that person A voted for candidate 1 to be able to verify the vote, so I think the answer to your question is "no".

To verify a vote, you need a few things:

1. Proof that all who voted were eligible,
2. A count of all voters who voted,
3. A count of all ballots cast,
4. Some system to ensure that the ballots that are counted are the same ballots that were cast, and
5. A mechanism for independent verification of the final tally of all ballots.

Having 1 means that each of the votes should count. Having all of 2, 3, and 4 means that no extra ballots are included in the count (no ballot stuffing occurred), and that no one's vote was skipped. Having 5 means that you can ensure that the count is reported truthfully.

Step 4 is the hardest to get right because, at some point, you just have to trust. I think you can really only get 4 by enforcing transparency in the voting process. Note, though, that if you have all 5, then the vote can be verified without knowing who voted for whom.

Ian

Nature does things for a reason.

Again, there is no evidence of this point of view.

I'm not sure how you got modded up. I can only assume the intelligent design folks somehow got points today.

First, I should make it clear that I think "Intelligent Design" is bunk, and I accept as fact that life evolves. Given that, my understanding of evolution permits "Nature does things for a reason" as an imprecise way of describing survival of the fittest. It's possible to imagine an ancient mammal or pre-mammal without this p21 gene that could regenerate. If a mutant showed up with the p21 gene and was fitter for it, then the gene would proliferate and nature's "reason" for the proliferation is that the gene is useful. Similarly, maybe salamanders "lost" p21 because of a useful mutation, and you could again interpret that as nature "having a reason" for the elimination of the gene from the salamander's gene pool.

I'd agree that "Nature does things for a reason" sounds a little like Intelligent Design because anthropomorphizing nature makes it seem like the speaker believes in an intelligent agent with motivations and "reasons", but it's a bit pedantic to assume that's the only possible interpretation.

Ian

I think I get your point, but I also think you've missed a point: a 1024-blade razor is probably incrementally better than a 1023-blade razor (for some value of "better"). On the other hand, a 1024-bit key is twice as good as a 1023-bit key. Unless I've forgotten my 3rd-year CS courses, factorization difficulty is exponential in the number of bits, so things get harder really quickly. Of course, Moore's Law is also exponential so, in theory, the time from "use 256-bit keys" to "use 512-bit keys" is about the same as the the time from "use 512-bit keys" to "use 1024-bit keys", but that sort of rebuts your comment. If Moore's Law continues to hold, then the arms race continues, but it remains easier to compute and store a key of arbitrary size than to crack a key of the same size. If Moore's Law becomes a wistfully-remembered relic, then the arms race is over and there's a well-known key size that's easy to generate and store but hard to crack. The only way for the cracking side to win is to find an efficient way to factor large integers. Quantum computing is a potential option, finding a general solution to NP-complete problems is another. Neither seems imminent.

I didn't RTFA, and the other comments in the discussion make me skeptical anyway, but your post seems to contradict itself. If the Traveling Salesman Problem is NP-complete (which I know to be true) and the Hamiltonian Path Problem is also NP-complete (which I assume is true from this discussion), then solving one problem is isomorphic to solving the other and a solution to either can be transformed into a solution to the other in polynomial time. If you'd be impressed "if they found the shortest path on an undirected graph with variable length edges", then you should be impressed with this, too (assuming they have found a solution as the summary indicates).

Ian