Donald Trump is slightly ahead of Hillary Clinton among likely voters in Iowa, according to two polls that were in the field this week. The latest Simpson College/RABA Research poll shows Trump beating Clinton by 44 percent to 41 percent in a five-way race, with 5 percent of respondents supporting Libertarian Gary Johnson, 2 percent each for the Green Party’s Jill Stein and independent Evan McMullin, and 6 percent unsure. Head to head, Trump leads Clinton by 46 percent to 44 percent.

Today Emerson College released Iowa numbers showing Trump ahead in a four-way race by 44 percent to 41 percent, with 5 percent for Johnson, 4 percent for Stein and 5 percent undecided. Emerson does not appear to have polled a two-way race.

Strangely, neither survey shows a large difference between men’s and women’s voting preferences in Iowa, despite data (and common sense) indicating that this year’s presidential race is shaping up to have the largest gender gap in history. RABA Research found men break for Trump 46-37 in a five-way race and 50-40 head to head, while women support Clinton 44-42 in a larger field and 47-43 against Trump alone. Emerson College’s results: a 45-41 advantage for Trump among men and a 44-42 lead for Clinton among women. I find those numbers very difficult to believe.

I enclose below more findings and notes on methodology from the new polls. Most disturbing, from Simpson College/RABA Research: only 66 percent of respondents said “Americans are ready for a woman to be president.” Some 20 percent said Americans are not ready, the rest were unsure. The cross-tabs show 37 percent of Republicans, 25 percent of Iowans over age 65, and 26 percent of those without a college degree say the country isn’t ready for a woman president.

Don’t forget to enter Bleeding Heartland’s election prediction contest.

At least a third of Iowans who will vote this year have already returned their ballots. Click here for tables showing the latest early vote totals. Iowa Democrats will go into election day with a significant absentee ballot lead, but smaller than the cushion Barack Obama had in 2012.