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I have seen few well-known related papers on online voting : DRE-i, DRE-ip and this one.

They have explained most of the process such as vote casting and vote tallying. But I did not find when and where they have found which party has received how many votes and who wins.

I think I am missing something very basic. Can somebody point me where and how it is done in these papers?

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  • $\begingroup$ Is there something unclear in 2.4.3. Tallying phase of DRE-i? $\endgroup$
    – fgrieu
    Commented Apr 28 at 8:21
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    $\begingroup$ Yes, for DRE-i, it is clear now. Can you please tell about DRE-ip as well? In DRE-ip, in tally phase, they just verify the tally process but do not tell the winner and who got how many votes. I think I am missing something there also. Please help. $\endgroup$
    – user60588
    Commented Apr 28 at 12:07
  • $\begingroup$ The description of the Tallying phase of DRE-ip is for the case where the voter's choices are limited to yes (1) or no (0), and the total number of yes votes is the sum of the votes $s$. Is your issue with going from that model to actual voting for two or more candidates? I'd be glad to discuss that (and criticize the systems on multiple grounds). $\endgroup$
    – fgrieu
    Commented Apr 28 at 14:41
  • $\begingroup$ Yes, I am looking for multiple candidates and count for each. And each vote has a kind of weight and not just in binary. Count for each is also something I am trying to find. Can you please see if you can provide some insight to a related question as well? crypto.stackexchange.com/questions/111604/… $\endgroup$
    – user60588
    Commented Apr 29 at 2:07
  • $\begingroup$ For DRE-ip, in Section 3 (proposed solution), 2nd para, they say, "We describe DRE-ip for the case where there are only two candidates, ie for vi representing the vote of the i-th ballot, we have vi in {0, 1}". But, later in the same section under Tallying Phase, they do not mention about who wins. Further, in section 6 (on multiple candidates), they reiterate that DRE-ip is for two candidates! I am not sure, but I think, it is for single candidate (similar to DRE-i) and not for two candidates. Otherwise vi=1 is for 1st or 2nd candidate? Please let me know if I am missing something here. $\endgroup$
    – user60588
    Commented Apr 29 at 5:42

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From a theoretical perspective we can turn a protocol for yes/no votes into a protocol for two candidates Alice and Bob with voters not having the option of a blank vote. We only need to make the question to "do you vote for Alice" (picked e.g. as the youngest of the two). The winner is Alice if an only if the number of yes vote is at least half the number of votes (with a tie advantaging the youngest candidate Alice). The voter's interface should show Alice and Bob rather than yes and no, to minimize bias.

For $n$ candidates with blank vote, we can conduct $n$ simultaneous ballots, with yes in ballot $i$ meaning voting for candidate $i$. The rule of not voting for more than one candidate (if we want that rule) can be enforced by the voting machine. The number of blank votes can be indirectly computed by subtracting the score of each candidate from the number of voters; or blank can be considered an extra candidate (allowing to detect small discrepancies, which depending on perspective is desirable or not).


Semi on-topic critic of the whole thing:

  1. Most voters won't understand the protocol, giving them a reason to not trust it. That contrasts inserting a paper bulletin in an opaque envelope, dropped in a transparent urn, where the vast majority of voters can get convinced that their vote is counted.
  2. Some will attempt to discredit the system using rational arguments that can't be rationally repelled. For example, that a quantum computer can break voting secrecy of the protocol (which is true for an hypothetical Cryptographically Relevant Quantum Computer that some profess will come rather sooner than later, so much that supposedly TLAs are busy Storing Now what they will Decrypt Later). Or that no proof is given to them that the RNG the voting machines are supposed to use is not replaced by a PRNG with known seed. Or that the hypothesis made that "the bulletin board is secure" in unwarranted.
  3. Voting machines introduce extra risks of breach of the secrecy of the vote, like electromagnetic leakage, or sound for early mechanical voting machines, much like a typewriter's sound leaks what's typed. Because such breach is conceivable, and the demonstration that it does not occur almost impossible to make for a computerized voting machine (including to specialists in cryptography and embedded security systems like me), it's at least conceivable to try to intimidate voters into voting as ordered or bribed, falsely pretending that such breach exists. Voting secrecy, and trust it in, are deterrent against voting under duress and bribery: a voter menaced or bribed to vote for X are more likely to vote for another candidate if they are very confident partisans of X won't know. Most of the complex voting ceremonial in countries will a long history of political elections (thus of voting intimidation and bribery) evolved from this fact. E.g voting booth with opaque curtains, opaque paper envelopes for the bulletins, multiple sources of valid printed bulletins, rules against counting marked bulletins, limitations of voting by mail or proxy, and more. BTW, whatever technical measure I have seen proposed or can imagine for mass voting at home is unable to deter duress or bribery.
  4. The part of the DRE-ip protocol where the voter "chooses to either audit the ballot or confirm her vote" is extremely unpractical. Also it opens the possibility for a voter to become convinced and get some tangible argument that the machine failed to produce the values that it should, even if that's not (it's enough for the voter to press the wrong voting button, in good or bad faith). In France, the law is essentially that the voter must NOT be able to audit if their vote is counted by the voting machine, with one rationale making it harder for a voter to cast doubt on the system.
  5. Despite best efforts of cryptographers, all machine voting protocols that I know require a high level of trust in the voting gear (with the least objectionable from that standpoint a proper Voter-Verified Paper Audit Trail). We don't know how to obtain that trust with confidence in an adversarial model where those that design and operate the machines are not trusted. And we even less know how to pass such trust to the bulk of the voting audience, which is perhaps the main point. The more complex and technical a voting system is, the easier it is to discredit with irrational arguments. Which works and is dangerous, as the the Jan. 6, 2021 invasion of the US capitol has shown.
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