Question: how will this idea fail?
Preferably in a way that is fundamental, and can't be easily fixed with small changes. And politically based, being unable to respond to problems because of the political system I describe
Currently, democracy works like this: you decide who or what you vote for, and you vote for that.
I offer to change it this way: during a vote you get assigned to a random partner, with whom you need to come to a common decision. If you manage to do so, your group vote is counted. If not, your group vote is ignored.
I imagine that this system could be set up as a response to increasingly divisive politics, with either existing parties becoming more extreme, or new extreme parties rising in popularity. Idea is that this method weakens all of the extreme views, as they are unable to find a common decisions with other people that don't share their view.
Another way for this system to be set up is for increased public education, as a way to show what politics is, a process of finding compromises. Assumption is that with such an experience people will be able to be more effective in many other fields as well as in their politics.
And one more option I see is a way to collect more and better data. Polls are unreliable in a sense that it can't measure the extent to which people are ready to go in order to get what they want. While measuring amount of not agreeing groups is easy and reliable, because not agreeing has a cost, that vote wont be counted. Assuming that people want their vote to be counted.
Why a random partner? Because bringing a friend will change nothing, even a person with most extreme views will have some agreeing friends.
Why just two people and not more? Because an average voter will have problems with even that. We used to vote alone, bringing consensus group size from 1 to 2 is already a large enough step. Only after this experience is fully tested I can imagine implementing larger groups.
Why ignore the vote of pairs that don't agree? Because otherwise there is no point. People will just vote the old way, and the new system will have no effect. There must be a profit in agreeing compared to not agreeing.
What if there is no common language? Internet translation, use friends who know the language or give up. Any sort of selection, like language, will allow people to break the system and vote the old way, from the comfort of their agreeing friends nearby.
What about fraud, violence, vote buying, loss of privacy in voting, intimidation? It can be solved with separate decision submission from each person. One doesn't know what another one have sent. But only if they match they will be counted.
What about increased costs? Properly selected government can change the GDP by a few percents, equal to about ten working days per year. If the vote is limited to a few hours spent by the voters to make a decision together, additional cost might be smaller than benefits of better politics.