<a href="https://www.thenationalnews.com/tags/republicans" target="_blank">Republican</a> voters in the US state of New Jersey will vote for their candidate on Tuesday to challenge embattled Democrat Tom Malinowski in the House of Representatives. Mr Malinowski, who won the seat previously held by Republicans in 2018, faces dimming odds after he became the subject of a House ethics investigation following reports that he failed to report more than $600,000 in stock transactions. Former state Senate Republican leader Tom Kean Jr, the son of popular two-time Governor Thomas Kean, leads a crowded field seeking to challenge Mr Malinowski. Mr Malinowski defeated Mr Kean by 1.2 percentage points in 2020. "It was a nail-biter in 2020 and his district has become a little more favourable for Republicans. So it's going to be a significant challenge," said Benjamin Dworkin, director of the Rowan University Institute of Public Policy and Citizenship. And in Iowa, three Republican candidates are vying to be named the challenger to Democratic Representative Cindy Axne. Zach Nunn, former state senator, has been endorsed by numerous high-profile Republicans including former secretary of state Mike Pompeo. He is the only Republican candidate to have held elected office. Also competing for the Republican nomination are businesswoman Nicole Hasso and construction consultant Gary Leffler. In Montana, Ryan Zinke, who served as interior secretary under <a href="https://www.thenationalnews.com/world/us-news/2022/05/13/judge-refuses-to-drop-election-system-workers-suit-against-donald-trump/" target="_blank">former president Donald Trump</a>, is running for a newly created House seat that the state gained thanks to population growth and the once-a-decade redistricting process. South Dakota's conservative Republican governor, Kristi Noem, faces a challenge from Steven Haugaard, a member of the state's House of Representatives. The winners of each of those Republican primaries are favoured to win in November. Frustrations over California's rising <a href="https://www.thenationalnews.com/world/us-news/2022/06/03/hospital-church-school-cemetery-shootings-shadow-americans-at-every-stage-of-life/" target="_blank">gun violence</a> and murder rates will be on Democratic voters' minds when they head to the polls on Tuesday. Rick Caruso, a former Republican, is challenging US Representative Karen Bass and other liberal candidates in the Los Angeles mayoral election. Mr Caruso, a billionaire developer, has self-funded more than $30 million in the campaign. Crime has been the centrepiece of Mr Caruso's campaign, forcing Ms Bass to vow to put more police on the streets in the sprawling US city. Homicides reached a 15-year high in Los Angeles in 2021, and killings in the city in 2022 are on pace to surpass last year, the <i>Los Angeles Times </i>reported. <i>Reuters contributed to this report</i>