Demographics have shifted, opinions have changed, lies were exposed, and campaign violations were brought to light. We cannot make take any conclusions away from the first referendum. It must all be back on the table for a second referendum.
Any referendum which didn't have all the options on the table would fuel division, and leave some voters voting for an option they don't want. The only way to end the Brexit debate once and for all is to go back to the people for a second referendum, in which they are allowed to vote for a soft Brexit, a hard Brexit, or to Remain a part of the EU. This could be done in one of several ways. It could be a single question with three answers: Remain, accept May's deal, or reject May's deal and leave with no-deal. Or, it could take the form of two questions, the first being an in/out question. Then, once the votes were tallied and, if the public voted to leave again, the follow-up question would be put to the voters on whether they wanted May's deal or no-deal. Finally, the public could be asked one question with the same three options, but asked to choose their favourite, and second favourite option. This would be a fair and accurate way to ensure the government is moving forward in agreement with public opinion.
This sounds great in theory but it doesn't work in practice. Firstly, there are too many uncertainties with May's deal. The public still doesn't know what it is voting for. The 26-page document doesn't deal with the length of time Northern Ireland would remain in the customs union for. It also doesn't outline what a UK-EU relationship will look like down the road.  If we are to have a second referendum, we should avoid the pitfalls of the first and ensure the public knows all the details it is voting on. Secondly, a three-way question over which the public prefers, to leave with May's deal, to leave with no-deal or to remain, would split the Brexit vote. This would mean the referendum would be rigged in favour of Remain. A scenario could play out where 40% of the population vote to Remain, 30% vote for a soft Brexit, and 30% for a hard Brexit. Then Remain would win the referendum despite 60% of the British public voting to leave the EU.  Finally, if the second referendum were to follow a different structure, for example, a structure where voters nominate their first and second choice, or a structure with two questions on the ballot, or even two rounds of voting, there would have to be a public awareness campaign. The country does not have time to both plan a referendum and educate the public on an entirely new way of voting.
The public is split into three camps: remain, a hard Brexit and a soft Brexit. Give all three camps a choice on a second referendum to ensure the outcome is the will of the people.
This does work in practicality.