Of course, all of the requirements are essential to attaining adequate election integrity. However, guaranteeing a completely secret ballot is both critically important and quite difficult to achieve in practice. It must not be possible for any person, other than the voter, to know for sure how a voter voted. The easier part of this is that, if a voter does not want anyone to know how s/he voted, it must be possible for the voter to keep that information secret. The hard part is that, even if a voter wants to prove to someone else how they voted, they must not be able to do so.
Everyone readily agrees that they should be able to keep how they voted a secret if they wish to do so. However, the second equally important secret ballot requirement tends to be forgotten. The reason voters must not be able to prove to anyone else how they voted, even if they want to do so, is that it exposes voters to possible coercion to vote a certain way, and it flings the door wide open to vote buying. And yes, those things can and do happen if it is possible.
Coercion could be as simple as a domineering spouse dictating how their mate should vote. Vote buying is the greater threat and has myriad variants. South Carolina was the last state to recognize the importance of the secret ballot and adopted it in 1950 because of significant vote buying. The percentage of people voting dropped by about 12 percent when the gravy train ended, indicating that fraud had been even more widespread than thought.
France banned absentee ballots completely in 1975 when rampant vote buying was discovered on Corsica. It should be totally obvious that voters can easily prove how they vote with absentee or mail-in ballots simply by showing someone their ballot or photographing it. There is no way to this can be effectively controlled. Although there are many other very good reasons to not allow mail-in voting, the lack of ballot secrecy is the most obvious and dangerous. Mail-in voting renders vote buying both extremely easy and very hard to detect.
When voters vote at a properly staffed and managed polling place, there is at least a good possibility that a completely secret ballot can be guaranteed. When voters vote in the privacy of a voting booth and then directly drop their ballots into a ballot box, each voter is the only one to see their own ballot. If voters wish to keep how they voted secret, they certainly are able to do that. But what if a voter wants to prove to someone else that they voted a certain way? Thanks to progress and modern technology, that’s a lot easier to do than it used to be. Just take a quick picture of the ballot while in the voting booth using a cell ‘phone camera.
Imagine a vote purchaser intercepting voters in the parking lot on their way into a polling place. After negotiating the price, the purchaser hands the voter a cell ‘phone containing instructions on how to vote or just a picture of a sample ballot filled in the way the voter is to vote. The voter uses the same ‘phone to snap a pic of the actual completed ballot while in the booth. The voter returns the ‘phone to the buyer, the buyer verifies that the voter voted as agreed and hands the voter a cash payment. This type of operation might be relatively easy to detect and stop, but individual voters using their own cell ‘phones certainly would not.
It must be illegal for anyone to possess any device capable of capturing and/or transmitting an image or facsimile of a ballot while in the voting booth or ballot box area of a polling place. Penalties must be stiff, even for first offenses, and enforcement must be taken seriously. Notices should be prominently posted. Provisions could be made for people to check their ‘phones at the door and reclaim them on the way out.
Note that federal and state laws in all fifty states already prohibit vote buying. There are stiff penalties for both the buyer and the seller. These laws alone are not going to prevent this type of fraud, especially not with mail-in ballots. When political organizations are willing to spend more than a hundred million dollars just to influence one senate race, the motivation to buy votes as a more sure-fire and lower-cost alternative obviously is intense.