If you were an Illinois voter taking a look at a sample ballot for the primary election for your district, the two parties would look relatively similar. Both parties have a line to vote for the candidate of your choice for President. Both parties also have a line to vote for delegate candidates. The Democrats have more delegate slots, so you get to vote for more delegate candidates on the Democratic ballot, but — other than that — the ballots look the same. The problem, however, is that the rules of the two parties dramatically change the meaning of your vote (and the “best” way to vote) depending upon which party’s ballot you choose to vote.
If you choose to vote the Republican ballot, the two lines are entirely separate election. The “presidential candidate” line only matters for the fifteen state-wide delegates who will be bound winner-take-all to whomever finishes first. However, the Republican Party rules exempt delegates from being bound by the presidential vote if the delegates are directly elected. In Illinois, the district delegates are directly elected. As such for the fifty-four congressional district delegates (three in each district), the state-wide result is irrelevant and the three delegate candidates who finish first in the delegate vote will represent that district (and be bound to the presidential candidate that they pledged to support) regardless of how their candidate does in their district. Thus, the smart vote is to vote for all three of the delegate candidates pledged to support your candidate. More importantly, you need to vote for the delegate candidates.
If you choose to vote the Democratic ballot, you are participating in what is commonly called an “open list” election. In an open list election, your vote for a party (or in this case a presidential candidate) determines how many seats/delegates that party/presidential candidate wins. Your vote for the individual delegate determines where that delegate ranks on the list. Thus, on the Democratic side, voting for all of the delegates supporting your preferred candidate is a waste of your vote because it has no impact on where the delegates supporting your candidate rank among each other. On the Democratic side, you only have to vote for delegate if you care exactly who goes to the national convention. If you do, the best thing that you can do is treat the delegate part of the ballot as four separate contests (rather than one): 1) male Sanders delegates; 2) female Sanders delegates; 3) male Clinton delegates; and 4) female Clinton delegates. Depending upon how many total delegates your district has (the smallest district has four and the largest district has nine), voting for more than one or two candidates in each “contest” is essentially cancelling your vote out.
In short, the “strategic” way of casting your votes depends upon your party. A Republican must vote for delegates and should vote for all three delegate candidates pledged to their preferred candidate (even if they happen to know one of the other delegate candidates). A Democrat does not need to vote for delegates and probably should split their delegate vote between supporters of both candidates or cast less than all of their allotted delegate votes (assuming that they even have a preference among the delegate candidates).
The question is how well this information has been communicated to Illinois voters. It is easy to see how Republican voters might assume that their presidential preference would determine how many delegates their candidate gets and that they are merely choosing which of their candidate’s delegates will get that slot. Similarly, it is easy to see how Democratic voters might assume that they need to vote for all of the delegate candidates who have pledged to support the voter’s preferred presidential candidate. In 2012, Republicans seemed to get the message with only two districts in which the winning candidate did not sweep the delegate slots. Similarly, in 2008, the Republicans only had two split districts. However, the Democrats did not seem to get the message with the delegate candidates pledged to each candidate tightly bunched and most of them getting a very high percentage of their presidential candidates vote. Whether the Republicans are doing a better job at communicating their rules or whether their rules are simply the way that people vote in most election, it seems likely that the Republican delegate results will essentially transform the Republican primary into a winner-take-most primary. However, if the three anti-Trump candidates could trust each other (and get the message to their supporters), the anti-Trump candidates could use the rules to get a 1-1-1 split in most of the districts, putting a major dent into Trump’s chances of winning the nomination.