When a reporter asked us why Louisiana, Missisissippi, New Jersey and Virginia have state elections in odd-numbered years, Tim Storey and I replied that it was probably the same reason that states have moved their gubernatorial elections into non-presidential election years: to insulate them from national political trends. After doing some research, though, it turns out that the reasons are sometimes more prosaic and quirky.
In some cases, the odd-year elections have to do with when new constitutions were adopted. Until the mid-19th century, the Virginia General Assembly, not the voters, elected the governor. A new constitution was adopted in 1851, and the first governor was directly elected in December 1851. They have been holding state elections in the odd-numbered years ever since. (See “Virginia’s Off-Off-Year Elections.”)
Louisiana adopted its Constitution in 1879. Alfred “Butch” Speer, clerk of the Louisiana House, reports this history of elections:
For scores of years we conducted our party primaries in the winter of the odd numbered years, with any necessary 2d primary held in January. Because Republican voter registration was so miniscule from 1877 until 1980, the general elections were mere irritants to the Democrat primary victor. Once we scrapped the partisan primary system  we set the entire system up to run in the fall of the odd numbered year, our traditional election season.
In New Jersey, before a new constitution was adopted in 1947, members of the Assembly were elected to one-year terms, senators to three-year terms staggered so that one-third were elected each year, and governors to three-year terms. Because the constitution took effect in an odd-numbered year, new elections–with Assembly members now serving two years and senators and governors four years–started in odd years and have continued ever since. Interestingly, though, this case provides some evidence of the desire to insulate New Jersey politics from national trends. Gov. Alfred E. Driscoll testified before the constitutional convention as follows:
…the election for a Governor and for Assemblymen should not coincide with a Presidential election. The importance of a gubernatorial election merits an election that will not be overshadowed by a national contest for the Presidency. The problems confronting the State are frequently distinct from those confronting the nation…
The origins of Mississippi’s odd year election are less clear. The Magnolia State appears to have held odd year elections since the 1830s.