With the Lok Sabha, the lower house of Parliament, securely in the hands of the Bharatiya Janata Party (BJP) and its allies, the locus of political opposition is set to move to the Rajya Sabha, the upper house, where the BJP remains in a minority. Most bills need to be passed by both houses to become law, and this has sparked speculation as to how the BJP might push through its legislative agenda without a Rajya Sabha majority.

It is evident from the chart below that the the United Progressive Alliance (UPA) controls many more seats in the Rajya Sabha than does the BJP-led National Democratic Alliance (NDA).

There are two obvious paths before the BJP:

1. Regional parties. The ruling party could make deals with unaligned regional parties (such as the Biju Janata Dal and the AIADMK) to win support for specific bills. Since the NDA is 59 seats short of a majority it will have to convince six or seven of the largest regional parties to support it in the Rajya Sabha.
2. Joint sittings. The BJP could arrange for joint sittings of the two houses under Article 118 of the constitution. The NDA is slightly over the halfway mark of the two houses’ 777 combined seats. However this is a rare step, carried out only thrice in Indian parliamentary history, and would require the consent of the President of India.

With two ordinances passed in its first two days, the Modi government has signalled that it may not be overly concerned about precedent. Even so, frequent joint sittings of the two houses could anger opposition parties that have become quite efficient at disrupting parliament in recent years.

The desirability of each strategy depends in part on how the number of seats controlled by the NDA grows over the next five years. If the NDA can woo new allies easily then it is less likely to take recourse to the more drastic step of calling joint parliamentary sessions. Recall that the Rajya Sabha reflects the balance of power in India’s states, and that a third of its members are elected every two years.

How then might the balance in the Rajya Sabha shift in the coming years? Let us assume that the NDA’s strong 2014 Lok Sabha performance translates into state election victories in 2014 (Delhi, Haryana and Maharashtra), 2015 (Bihar) and 2016 (Assam) in roughly the same proportion. This is a contestable assumption because the national level “Modi wave” will have less relevance in a state election in which local factors gain prominence.

Still, maintaining that assumption, here is what the Rajya Sabha might look like in 2016 (excluding the 11 current vacancies in the upper house):

This is quite clearly not enough to tilt the scales in the NDA’s favour. Even after the 2016 Rajya Sabha elections, the ruling alliance will be 47 seats short of a majority and will need the support of regional parties such as the Samajwadi Party and the All India Trinamool Congress.

The NDA’s prospects begin to sharply improve in its fourth year if the 2014 election results are mapped on to state elections in 2017. Keep in mind that this is a very optimistic scenario for the alliance: the BJP’s popularity could well have ebbed by then and the local factors mentioned above will again be in play in a state election. We are also assuming that party state assembly seat shares translate quite simply into Rajya Sabha votes; in practice there is often voting across party lines and strategic voting in favour of third candidates that can make the outcome less predictable.

But assuming that the broad patterns of the general election apply to the 2017 state elections in Goa, Gujarat, Himachal Pradesh, Manipur, Punjab, Uttar Pradesh and Uttarakhand, this is what the Rajya Sabha could look like in 2018:

The NDA is still 30 seats short of the halfway mark in the Rajya Sabha, and the ruling alliance will need to win over at least one of the three biggest regional parties (Samajwadi, Trinamool and AIADMK) plus an assortment of smaller players. The NDA is well over the halfway mark of a joint sitting at this point, so its preferred strategy will depend on how easily it can woo those parties.

Either way, the NDA will remain short of a majority in the Rajya Sabha, although its rising tally will require it to attract fewer allies by 2018. But 2018 is close to the end of the its term, which means that for most of its tenure the NDA will be forced to reach out to a large number of regional parties to pass bills in parliament.