Gillibrand's U.S. Senate Seat Attracts Another Republican Candidate Joe Carvin, the Republican supervisor in the Westchester County town of Rye, announced on Wednesday that he would run for the United States Senate in New York, seeking to unseat Kirsten E. Gillibrand, a Democrat. In a statement, Mr. Carvin, who runs a hedge fund and who has twice been elected the Rye supervisor, said he decided to seek the position out of concern over the dire state of the country's economy. "I believe that our representatives in Washington have provided us with an economic framework that severely undermines our competitive position in the world today," he said in the statement. "If we do not act now, and with urgency, our competitive position risks dramatic deterioration."" The decision by Mr. Carvin adds to the already crowded field of little-known Republicans who are seeking their party's nomination to run against Ms. Gillibrand, who is in her first term. Earlier in February, Wendy Long, a Manhattan lawyer who was legal counsel to the Judicial Confirmation Network, a conservative organization, announced that she was seeking the nomination. In addition, George Maragos, the Nassau County comptroller, entered the race a few months ago. Republican leaders have been searching for a candidate to take on Ms. Gillibrand, who they believe would be vulnerable against a strong challenger. But no big-name Republican has stepped forward and party leaders have not coalesced around any of the existing candidates. A former House member from upstate New York, Ms. Gilibrand has been working hard to establish a statewide presence since 2009, when Gov. David A. Paterson appointed her to the Senate seat vacated by Hillary Rodham Clinton, who left to become secretary of state. In 2010, Ms. Gillibrand won election on her own, allowing her to complete the unexpired portion of Ms. Clinton's term. This year, Ms. Gillibrand is running for a full six-year term.