Two‐stage decision‐making within the firm: Analysis and case studies

This article analyses, with case study illustrations, a two‐stage decision support technique for making informed choices within firms. The technique can assist managers by the use of simple decision‐tree diagrams, assigning values to its branches. The technique is based on the microeconomics of choice orderings, and we demonstrate how appropriate decision trees can be constructed and applied. This technique is illustrated by three case study vignettes based on real actions of UK firms. These show how such decision trees can both aid our understanding of choices made and assist in the practice of choosing financial reporting regimes and techniques.


| INTRODUCTION
This paper applies the microeconomics of preference orderings and decision trees to view firms' choice behavior through the theoretical and empirical lens of two-stage decision-making (Bhargave et al., 2015;Li et al., 2014;Xie & Lee, 2015). It illustrates this modelling approach using a set of three UK case studies, in which the two choice variables are financial reporting regimes and techniques. Our theoretical framework allows us to investigate whether a company's decision-making process is sequential (in two senses) or nested/ simultaneous (Birnbaum, 2010;Colman & Stirk, 1999;Hensher, 1994) and-if sequential-whether a firm chooses its financial reporting regime, or its techniques, first. Our case studies (Cooper & Morgan, 2008), founded on fieldwork within several UK companies, a methodology well respected in managerial economics (Rubin & Dnes, 2010), enable us to illustrate thoroughly how, in practice, the detailed attributes of decision-making develop (Trotman et al., 2011).
Thus, our use of theory is viewed empirically, through fieldwork evidence on how two-stage decision-making works in practice, considering such key features as exposure to risk, complexity of financial reporting and the time pressure of commercial and regulatory deadlines.
An early insight of Simon (1959) was that companies, like individuals, have preferences, which allow them to order alternatives, for example, over goods, strategies and techniques. Subsequently, Simon (1979) added a further insight which is relevant to parsimonious decision-making in this article-that although human actors rationally seek a best outcome, there are limits to human cognition, like memory, calculation and reasoning, which make rationality bounded.
Humans often use heuristics to overcome this bounded rationality.
Two-stage decision-making, as deployed in this article, is an example.
To illustrate, it is a common method in job recruitment, where a first sift of candidates is made, using broad criteria, like qualifications, followed by a second sift, which uses more focused criteria like prior workplace experience. In our case study illustrations, we investigate how firms make choices over (1) financial reporting regimes like the International Financial Reporting Standards (IFRS) or the Generally Accepted Accounting Practice in the UK (UK GAAP) and (2) techniques to implement them, like market or cost approaches to valuing intangibles. This follows up on the insights of Simon (1959Simon ( , 1979 by suggesting how the heuristic of two-stage decision-making can help to solve this important decision problem. Two-stage decision modelling will be familiar to many regional economists through optimal location models. In the case of housing economics, the two-stage modelling might involve (1) the move-stay decision and (2) the destination choice decision. A variant of this is an intra-urban two-stage model, with (1) choosing a neighbourhood and (2) choosing a dwelling place. In Haynes and Fotheringham's (1990) article, the modelling is explicitly econometric using variants of logit/ tobit choice models.
In managerial economics too, the two-stage approach has been found useful. Typically, it has been implemented in schematic, rather than econometric form, often using flow diagrams. For example, Arogyaswamy et al. (1995) model firm turnaround using stages (1) 'halt decline' and (2) 'implement recovery'. Wu et al. (2005) assess the performance of online firms using the stages (1) 'web site visits' and (2) 'view to buy'. Finally, Gaston-Breton and Martın (2011) adapt a generic 'screening and selection' two-stage model for decision support in identifying (1) the most suitable country in which to market a product and (2) the best market niche within the country.
The approach of our article lies more on the managerial economics spectrum, with its emphasis being decision support, rather than positive economics. It advocates the sketching of simple decision trees to display alternatives clearly, and to use them for decision support by attaching values to such alternatives, using the calibrated 'stated preferences' of agents within the firm, like owners, employees and managers. The two-stage decision problem we model in this article is of how the firm (1) chooses a regulatory regime under which to report financially and (2) chooses the technique(s) by which reporting is accomplished.
In commending using this tool, we recognize that such models should not be applied mechanically, but rather should be used for decision support, with a healthy injection of complementary evidence, including hard data and human observation. In this context, Khan, Dhar and Wertenbroch (2005) have warned us not to overemphasize 'utilitarian criteria', which relate solely to the functional aspect of running a business (like spreadsheets), to the neglect of 'hedonic criteria', which relate to experiential and discretionary aspects of running a business (like motivational management). An advantage of two-stage modelling, as emphasized by Bhargave et al. (2015), is that it lends itself to balancing the utilitarian and hedonic. In their article, they indicate through three case study vignettes the way in which decisions can be made, balancing the utilitarian and the hedonic. This maintains principles of logic, without neglecting human characteristics and the business environment of the firm, in a social, regulatory and economic sense.
These mathematical tools remain important in economic theory (Mandler, 2020) and are a part of modern developments in cryptography (Dragon et al., 2018). They will be used in this article to explain how companies make choices over financial reporting regimes and the techniques that support them. Our approach treats such corporate decision-making as a two-stage decision problem.
The structure of our paper is as follows. Section 2 covers the theory and models of this article, covering microeconomic choice theory, and Section 3 explains the fieldwork methods by which primary-source data in the United Kingdom were obtained. In Section 4, a private firm's (Company Alpha) decision-making process across time is elaborated, in terms of its use of a sequential choice mode. By contrast to this private company, Section 5 illustrates a public firm's choice behavior (Company Beta) for a nested choice mode, given free choices, and discusses its sequential choice mode when choices are tied. Finally, a third case study illustration is provided, in Section 6, again of a public company (Company Gamma), which is used to compare findings with those in the previous two sections, with an emphasis on ease of execution and transparency. Section 7 further discusses the three case studies and summarizes the findings, and Section 8 concludes this paper.

| MODELS OF SEQUENTIAL AND SIMULTANEOUS CHOICE
This section expounds briefly, generally shorn of technical exposition, the bare bones of sequential and simultaneous choice making in microeconomic theory. Underpinning this approach is the presumption that individual preferences drive choosing behavior. We discuss ways in which choices are made sequentially, as a prelude to showing how in practice (see Sections 4-6) such theory can be applied to choices over financial reporting regimes and the techniques that support them. On these theoretical foundations, choosing behavior is developed in terms of ways of making decisions when sequences are essential (e.g. choosing a financial reporting regime before choosing the technique that supports it; or choosing a technique that matches existing skills, then choosing the financial reporting regime in which it can be best deployed).
This leads to a theoretical framework that permits the analysis of two-stage decision-making in lexicographic (Lex) or co-lexicographic (CoLex) terms: informally, ordering like books in a library (Lex), or the converse (CoLex) (Colman & Stirk, 1999;Dragon et al., 2018;Harzheim, 2005;Houy & Tadenuma, 2009). Thus, we will show how sequential decisions can be analysed in terms of decision trees that display potential decisions at each stage, and the payoffs (in terms of net or ratio utilities) that are attached to each potential action, as represented by a branch within the decision tree.
As mentioned before, companies also have preferences over various alternatives (Simon, 1959). For example, firms have preferences over financial reporting regimes, each one being a whole system of accounting standards, such as IFRS. Similarly, it might have preferences over financial reporting techniques, each one of which is a detailed accounting method allowed within a specific regime, such as the fair value approach to valuing investment properties. In this paper, two types of preference orderings, lexicographic (Lex for short) and the co-lexicographic (CoLex for short), are introduced (Dragon et al., 2018;Harzheim, 2005). The Lex approach works like ordering books on a shelf in a library. For example, suppose preferences for shelving books in order can be denoted by the inequality sign (<). When applied to word strings for book titles, an ordering might be expressed by something like a < aa < aaa < ab < aba. This would be used to order five books in lexicographic on a shelf. As we shall see below, the CoLex approach is in a sense the converse or mirror image of the Lex method. We will use Lex and CoLex concepts to help us explain how companies make accounting choices over regimes and the techniques that support them. Our approach treats such corporate decisionmaking as a two-stage choice problem.

| Lexicographic (Lex) ordering
Consider Sets X and Y, whose elements will be used by personnel within the firm (e.g. the financial or accounting director) to make decisions (e.g. about regimes and techniques). Let X = (x 1 , x 2 ) and Y = (y 1 , y 2 ), where x i and y i are corresponding utilities of X and Y. If an individual's preference follows a lexicographic order, X is preferred to Y if and only if x 1 > y 1 or x 1 = y 1 and x 2 > y 2 (Colman & Stirk, 1999;Harzheim, 2005;Houy & Tadenuma, 2009).
In the framework of a two-stage choice model, we suppose x 1 and y 1 are the utilities of choice in the first stage, and we regard x 2 and y 2 as the utilities of choice in the second stage. In this situation, if an individual applies a lexicographic ordering, it implies that he or she first deals with the choice problem of the first stage (i.e. considering utilities x 1 and y 1 ) and then determines the options in the second stage (i.e. evaluating utilities x 2 and y 2 ). This decision-making process involves a sequential choice, which moves from the first stage to the second stage. Existing literature (Birnbaum, 2010;Colman & Stirk, 1999) on this kind of sequential behavior emphasizes that when choices in the first stage are perceived as more crucial than those in the second stage, people tend to make decisions in a lexicographic order.

| Co-lexicographic (CoLex) ordering
Though, a less well-known preference ordering, the co-lexicographic (CoLex) ordering, Dragon et al. (2018), is useful to our purpose. In a sense that will become clear, this ordering compares choice sets in the opposite direction to the lexicographic (Bekmetjev et al., 2003).
Considering again the distinct sets X = (x 1 , x 2 ) and Y = (y 1 , y 2 ), a co-lexicographic (CoLex) ordering implies that X is preferred to Y if and only if x 2 > y 2 or x 2 = y 2 and x 1 > y 1 . A person with CoLex preferences considers the choices listed in the second stage (i.e. comparing utilities x 2 and y 2 ) before making decisions about the choices in the first stage (i.e. comparing utilities x 1 and y 1 ). In this sense, he or she goes in the opposite direction to the person with Lex preferences. Similarly, although the CoLex choice pattern is sequential, the sequence is the exact opposite of the Lex choice pattern, starting from the second stage.
Although lexicographic (Lex) orderings play an important role in theories of choice in microeconomics, there has been very little research in corporate decision-making, which uses, or applies, this concept. To the best of our knowledge, only one study has attempted to analyse corporate choices using lexicographic orderings. This is in an experimental study of decision-making in auditing by Uecker and Kinney (1977). They illustrated how practitioners might prioritize certain rules and discovered that Lex orderings were used when making auditing judgements. So far as we know, no study has yet explained a firm's reporting choices by CoLex preferences.

| Nested choices
In addition to the Lex and CoLex preferences, other decision-making patterns are possible, of which the most important is that individuals might elect options from both stages simultaneously (Hensher, 1994;Tu & Goldfinch, 1996). In our paper, this will be called a nested or un-staged choice. An analysis of livestock markets by Bellemare and Barrett (2006) illustrates how the nested choice pattern can arise in a two-stage model. In their work, the first stage was deciding whether to enter a market, and the second stage was the transaction amount. They found evidence of both staged (i.e. sequential) and simultaneous (i.e. nested) behavior, and their empirical evidence suggested that the sequential choice pattern leads to a better outcome than the nested.

| Financial reporting regimes and techniques
We now take our discussion of two-stage decision models into the practical domain. If a firm first chooses the ith financial reporting regime (X i ) without considering the technique choices and then chooses the jth technique combination (X ij ) under this chosen regime, this will be our first type of sequential choice (from stage one to stage two). This is a Lex decision-making process. In this situation, this firm chooses from the choice set of financial reporting regimes {X 1 , X 2 , …} selecting the one that generates the highest utility u (X i ) = x i . It then chooses the technique combination with the highest utility, which we denote as x ij . Each accounting choice X ij can be considered as an ordered set X ij = (x i , x ij ), where the first utility x i is related to the regime choice and the second utility x ij is associated with the choice of technique combinations. The utility of an accounting alternative X ij will be determined by the utility of the relevant regime choice and technique choice and can be expressed as a (joint) function of regime and technique utilities, u (X ij ) = f(x i , x ij ). Because all technique combinations under regime i will share the same regime utility x i , this firm now only needs to compare the second utility x ij under this chosen regime.
Furthermore, the utility associated with technique combination x ij is a function of utilities of different techniques for treating various parts of financial reports. This can be expressed as where the k-index denotes different financial reporting techniques, used in different parts of financial reports.
Consider now the second-type sequential choice: Suppose now the company first selects techniques and then decides its regime. Its decision-making process starts from the second stage and moves on to the first stage. That is, this firm follows a CoLex preference ordering when choosing accounting modes. The company first considers the utilities of technique combinations x ij = f(x ijk ), where the argument of function f(.) is a vector of techniques, indexed by k. After electing the technique combination with the maximum utility, this firm determines its financial reporting regime by comparing utilities of regimes {x 1 , x 2 , …}.
The third type of choice behavior, in the two-stage choice model context, is called a nested choice or a simultaneous choice. In a nested choice (Nest), the firm considers and evaluates all available choices of regimes and techniques and chooses the accounting mode X ij , which maximizes the utility u (X ij ) = f(x i , x ij ). When choosing the accounting mode X ij , this company determines its regime and technique simultaneously. The firm does not make reporting/technique choices in stages, and the nested choice is derived from balancing the utilities of regimes and techniques. It is when the relative importance, in utility terms, of regime choices and technique choices is not evident that a company tends to make such decisions simultaneously. Although there is no specific preference ordering to express the nested choice, this decision-making process is often discussed in choice studies (Bellemare & Barrett, 2006;Hensher, 1994), as it presents a rational alternative to staging.
For assistance in understanding our subsequent analysis of the three case studies, Table 1

| FIELDWORK METHODS
Our methods combined administered questionnaires and fieldworkbased interviewing (Reid, 2015) to gather UK data on individual preferences at the corporate level. This allowed us to calibrate preferences in terms of utilities. Utilities so derived are called 'stated preferences', being acquired directly from the person making the choice (typically the financial director of the firm) rather than indirectly from market data (e.g. via a 'demand curve') (Adamowicz et al., 1994;Hensher, 1994;Reid & Smith, 2007a, 2007bSchipper, 2010). These utilities permit calibration (typically by a 5-point Likert scale) of perceived benefits (B) and costs (C) of choices made, which in turn can be used to calculate net benefits (B − C) or ratio benefits (B/C), in utility terms, of actions taken by financial directors over regimes and techniques.

| Choice behavior
Combining theory and methods allows us to consider choosing behavior in terms of alternative ways of achieving complete choices in two stages, or alternatively to consider choices as being intrinsically simultaneous (or 'nested') (Birnbaum, 2010;Colman & Stirk, 1999;Hensher, 1994). These choosing modes will be explored empirically in this paper using three illustrative corporate case studies from the United Kingdom (see Sections 4-6), which display a revealing range of rational choosing behavior, including their effects over different time horizons.
Based on the methodology of stated preferences (i.e. preferences elicited by direct interviews with individuals, rather than deduced from market data) (Adamowicz et al., 1994;Hensher, 1994;Reid & Smith, 2007a, 2007bSchipper, 2010), our research obtains UK firms' perceived costs and benefits of adopting financial reporting regimes and techniques by two instruments: an administered questionnaire and a semi-structured interview agenda (Cohen et al., 2002;Wengraf, 2001). From the perceived benefits (B) and costs (C) of adopting regimes and techniques, expressed as perceived utilities and dis-utilities, obtained by these instruments, using Likert scales, companies' net (B − C) and ratio (B/C) utilities of implementing regimes and techniques were calibrated. These net and ratio utilities allow us to examine companies' decision-making in our two-stage choice model of financial reporting regimes and techniques by the development of three illustrative case studies (see Sections 4-6) (Cooper & Morgan, 2008).

| Instrumentation
Our instrumentation builds on research by Reid andSmith (2007a, 2007b) in which the stated preference approach was applied to examine willingness to adopt Financial Reporting Standard for Smaller Entities (FRSSE). In the current context of regimes and techniques, the financial director would be asked, for example, what the benefit of a regime was on the scale: N/A, zero, low, medium, high or extreme. This is then coded as 0 for not applicable, 1 for zero, 2 for low, 3 for medium, 4 for high and 5 for extreme.   More detailed narrative analysis of choosing modes was accomplished by using, in addition, face-to-face interviews. These used a semi-structured interview instrument with a 3-point agenda: ( More on the forms of our instrumentation are provided in Appendix S2 and Data S2.

| Sampling
The fieldwork was conducted in the United Kingdom (in 2014), with site visits to the firms analysed in this paper, for face-to-face interviews using a three-part semi-structured interview agenda (see Appendix S2). The firms were a mix of public and private businesses. The person interviewed was always senior, but each could have a different status or role within the firm, for example, Financial Director, Head of Finance, and Company Secretary. For clarity of exposition, we have standardized on using 'interviewee' for all such persons throughout the empirical parts of the paper. Cross-checks with interviewees, post-interview, allowed resolving of facts, anomalies or inconsistencies with the interviewees revealed in fieldwork debriefing. These checks also allowed for requesting further data and narrative from the interviewees to corroborate and/or amplify what was said in the interview. Interview data were supplemented with public domain data to help build contextual material for our case studies.
Further, we carried away a considerable volume of internal pamphlets/ memoranda/guidebooks/promotional material from each firm, adding to the understanding of their corporate operations. The whole body of data were encrypted for anonymity. We have chosen a judgement sample of the three companies which best represent our taxonomy of Lex, CoLex and Nest (see Sections 4-6). These firms are named (for confidentiality) Companies Alpha, Beta and Gamma, respectively. These are illustrative case studies in vignette form (Yin, 2018). As vignettes, they are not exhaustive, but they are detailed and do give a good flavour of decision processes in real firms, as regards financial reporting choices. Further information on these firms is available in Data S1. can be found in Figure 1. This figure shows accurately the main financial reporting regime choices (indexed i) at the apex, and their respective utilities (X i ), using stated preferences. Then going down the pyramid, we show further possible technique combinations choices, indexed j and represented figuratively rather than literally because they are numerous, and their respective utilities (X ij ), again just figuratively. In the event, Company Alpha did adopt UK GAAP, which is consistent with it having a higher adoption utility than under IFRS (see Figure 1a). In the parentheses shown in Figure 1, ratio utilities are given first, followed by net utilities. It can be observed that adopting IFRS would lead to a ratio utility (B/C) of 0.5 and a net utility (B − C) of −2. Using UK GAAP and FRSSE both generated better ratio (0.67 > 0.5) and better net utilities (−1 > −2). FRSSE was only relevant to subsidiaries (see Figure 1c). 2 The downward pointing arrow to the right in Figure 1 indicates that the decision-making sequence was from financial reporting regime choices to technique choices. This is the sequential mode of two-stage decision-making.  Figure 1), which is to say its decision-making was lexicographic (Lex).

| Co-lexicographic (CoLex) ordering
The context of this subsection is that when the Financial Reporting To augment the mere denoting of choices in Table 2

| Summary on Company Alpha
In this illustrative case (see Figure 2), which is specifically related to Company Alpha's decision-making processes were sequential in both cases, with procedures mainly relying on judgement, rather than naked science-like spreadsheet modelling. As indicated by the interviewee of this company, it was simpler for them to make decisions using staged and subjective approaches (Burmeister & Schade, 2007;Einhorn & Hogarth, 1981).
Regarding the characteristics of the decision-making process, although regulated by relevant authorities to produce financial reports, the company was not under great external time pressure to do so. In this case, time pressure arose mainly from internal rather than external influences, and the company had its own schedule for financial reporting. Reflecting little time pressure, Company Alpha did not regard speed of preparing financial reports as crucial to making accounting decisions. The interviewee said that ease of execution was more important than transparency. This might be because Company Alpha was a private firm whose financial reports were aimed at internal control rather than at attracting external investors. The flavour of their internal processes was as follows: (1)  To advance the investigation further, we asked our interviewee whether they thought the un-staged process and the staged process would result in the same, or different, choice patterns. They replied that it depended on the importance of choices, because final decisions must meet the strategic goals of the company. This comment matches our early argument in this article-that the relative significance of technique and regime choices will themselves play a role in determine companies' preference orderings and their decision-making processes. The following paragraphs apply the theoretical concepts mentioned in Section 2 to formalize the nested choice process. If a company's choice is X ij , it means that the firm chooses regime i, which brings the utility x i , and technique combination j of this regime, which generates the utility x ij . Unlike companies that deploy sequential decision-making processes (i.e. only compare x i or merely compare x ij in the first instance), a firm using a nested process will consider all utilities of regimes and techniques together. Hence, the firm's utility function of a joined accounting mode could be formally presented as u(X ij ) = f(x i , x ij ). The company will assign weights to various accounting choices, including both regimes and techniques. The weights reflect the importance of these choices and influence the company's adoption utilities. The firm will choose the accounting alternative that leads to the maximum combined utility of the regime and the techniques.
For example, this company will elect the accounting mode X 12 (Regime 1 and Technique Combination 2) if the utility of mode u(X 12 ) is higher than u(X 11 ), u(X 21 ) and u(X 22 ). That is, Regime 1 and Technique Combination 2 yield the highest utility than other joint options.
With regard to the utility function, it should be noted that firms often pay more attention to those forms of financial reporting that help them to achieve their corporate goals. Firms have their own specific goals to meet, and the significance of each goal varies. Therefore, we would expect individual firms to prioritize accounting choices differently, resulting in diverse preferences and utilities towards accounting modes, being observed in our fieldwork sample. were not only about accounting but about how the entire company was run, of which just one aspect was accounting. This explanation also suggests that the nested decision-making process adopted by Company Beta helped it to find better solutions, in general, by viewing all decisions within the context of the health of the entire company.
In terms of attributes during the choice process, the interviewee of Company Beta said that there was always time pressure. Nonetheless, the interviewee said that the schedule was almost the same for every year, so in that sense was predictable. The interviewee added that it is a very complicated process to interpret regulations properly and to fully understand how the regulations influence the company.
Certain accounting procedures, such as those for the treating of intangibles and acquisitions, were found to be especially difficult to implement and understand. The interviewee said that these complexities slowed down the decision-making process. Because it is essential to meet deadlines and to have accurate financial reports, Company Beta tended to look for help from external experts, who assisted the company in making decisions quickly and professionally. Moreover, the interviewee indicated that the company preferred more evidence, rather than less, to make decisions and to conduct a thorough analysis.
Hence, most of the time, they did have 'to hand' the relevant data to support decisions. If they had to make decisions relatively quickly, they did so by judgement based on previous experiences (Burmeister & Schade, 2007;Einhorn & Hogarth, 1981 Beta tended to require more visible evidence to support its decisions (cf. March, 1987). Such supporting information was also useful to Company Beta in applying an un-staged decision-making process, which aimed to accommodate various key aspects of the entire firm's operations.
F I G U R E 3 Decision tree of UK public company Beta (individual accounts, until the end of 2014). (a) Utilities are in parentheses. Ratio utilities (B/C) first and then net utilities (B − C), for example, X 1 = 1.5 > X 2 = 1 in terms of B/C, and X 1 = 1 > X 2 = 0 in terms of (B − C) indicate that IFRS should be chosen over UK GAAP. (b) the double arrow indicates that this is a nested decision-making process 6 | PUBLIC COMPANY GAMMA: NESTED CHOICE  Figure 4 where the double arrow indicates a nested decision-making process.
This situation mimics how Company Beta responded to free choices, as mentioned in the Section 5. The utility function of a combined financial reporting mode, u(X ij ) = f(x i , x ij ), is relevant to the case of Company Gamma. Here, as before, the i subscript refers to regime, and the j subscript refers to technique. When it faced the free choices for individual accounts, Company Gamma chose the joint regime and technique mode X ij , which generated the maximum utility u(X ij ). The chosen accounting mode X ij , consisting of the regime utilities x i and the technique utilities x ij , was expected to achieve, overall, better outcomes for Company Gamma because it evaluated regimes and techniques at the same time. The weights that Company Gamma assigned to various accounting choices were said to be influenced by its goals and affected the form of its utility function.
The interviewee mentioned that individual accounts were perceived to be less important than consolidated accounts. Therefore, when Company Gamma was determining which accounting forms were best for its individual accounts, its criteria focused, first, on their ease of execution and, second, on their credibility-that is, it required that its financial reporting results should be perceived by its stakeholders to be reasonable. Furthermore, the interviewee pointed out that Company Gamma generally judged the benefits of various accounting modes subjectively. He also thought that regime choices and technique choices influenced each other mutually and were intrinsically linked. In addition, because regimes were converging and there was beginning to be no great difference among different regimes, we were told that Company Gamma did not examine choices in detail or in stages. Under these circumstances, it was easy to make decisions by the un-staged (viz. Nest) process. Using the un-staged procedure is consistent with Company Gamma's intention to complete tasks easily, with no downside on credibility.
We note that both Company Alpha and Company Gamma thought that the ease of execution was especially important during the decision-making process. Despite this concordance, Company Alpha applied the staged process, whereas Company Gamma used the un-staged process, when free choices could be made on financial reporting. As discussed in Section 4, Company Alpha determined that certain regimes or techniques were much more favourable than others. Nevertheless, Company Gamma felt, per contra, that formally distinct accounting standards were in fact very similar. These disparate outcomes suggest that if a business such as Company Alpha was eager to achieve the goal of choosing a specific accounting form, F I G U R E 4 Decision tree of UK public company Gamma (individual accounts, until the end of 2014). (a) Utilities in parentheses. Ratio utilities (B/C) given first, followed by net utilities (B − C), after the bar. The adoption utilities of UK GAAP were not available in this case. (b) the double arrow indicates that this was a nested decision-making process which resulted in regime choices being much more significant than technique choices (or vice versa), it would apply a sequential decisionmaking process. By contrast, a firm like Company Gamma would tend to use a nested procedure to make decisions, if its various available accounting modes were of almost the same utility and its regime and technique choices too were almost of equal importance.
When it came to the process of decision-making and how it is developed, the interviewee of Company Gamma said that its decisionmaking process was mainly judgement based (cf. Bonner (1999)), but with certain levels of procedure support, including financial computation and scenario analysis. Both Company Alpha and Company Gamma looked for ease of execution during the decision-making process, and both tended to make decisions subjectively. Differing, to a degree, from Company Alpha, Company Gamma's decision-making process was sometimes based on procedures that provided enhanced information for decision-making. Using a nested decision-making process (Nest) means that companies considered regimes and techniques together and they tried to accommodate all aspects of accounting choices. In this situation, numerical data and other practical forms of evidences would be helpful to companies for making decisions. Thus, interviewees for Company Gamma and Company Beta, which both made choices simultaneously when facing free choices, also both reported using supporting data to some extent in determine their accounting modes.

Further, the interviewees of Company Beta and Company
Gamma both stated they had to be sure that the results of financial reports met shareholders' expectations, when they evaluated accounting modes. Although the interviewee of Company Alpha mentioned shareholders as having an impact on accounting choices, it seemed this firm focused more on the ease of execution, and on simplicity, during the decision-making process than on pleasing shareholders.
One explanation for this difference might be the fact that Company Alpha was a private firm. However, Company Beta and Company Gamma, both of which were public firms, would probably have as much, or more, pressure from investors.
Additionally, the interviewee of Company Gamma indicated that transparency and compliance were very important when preparing financial reports. Financial reports also needed to be prepared and completed quickly. This focus of transparency might also be related to the company's public character. In terms of the characteristics in the decision-making process, the interviewee felt that the decision-making process was not complicated, because all financial reporting standards are converging. Only some parts, like financial instruments, foreign exchanges, and judgemental aspects, were, to them, particularly difficult. Moreover, they mentioned that the risk and the uncertainty (most of which come from transactions) would influence significantly the decision-making process. Company Gamma often used risk classes to calibrate degree of risk. The interviewee also stated that only during the period of transitioning to IFRS would Company Gamma come under time pressure. Because the process to prepare financial reports had become routine, Company Gamma had not often been subject to time pressure. Company Gamma also participated in educational training for staff to update their knowledge on accounting regulations and to discover what the necessary changes were.
Company Gamma usually had enough information to make rational decisions (cf. Simon (1979)

| FURTHER DISCUSSION
This article has developed a theoretical framework for analysing the choices made by firms confronted with options on financial reporting regimes and the techniques that support regimes. This framework uses a two-stage decision model, which distinguishes between lexicographic (Lex) and co-lexicographic (CoLex) decision modes (Colman & Stirk, 1999;Dragon et al., 2018;Houy & Tadenuma, 2009) and allows a nested alternative to both (Nest). The underpinning of this model is a subjective utility-based view of decision-making, which allows a calibration of preferences over regimes and techniques. The utility metric is based on a 'stated preference' approach (Adamowicz et al., 1994;Hensher, 1994;Reid & Smith, 2007a, 2007bSchipper, 2010), which allows the evaluation of alternatives in ratio utility (B/C) or net utility In brief, we investigated whether firms made decisions in stages, or all at once, when facing choices across both regimes and techniques (Birnbaum, 2010;Colman & Stirk, 1999;Hensher, 1994). If they determined the form of accounting reporting in stages, we asked them whether they dealt with the regime choice first or the technique choice first. The theoretical underpinning to our paper was developed through a formal model, as explained in Sections 1 and 2. This was elaborated with three case study vignettes (Companies Alpha, Beta and Gamma), with supporting graphics and narratives in Sections 4, 5 and 6, respectively, in which three alternative decision-making modes were displayed by decision tree graphics based on the elicited 'stated preferences' of companies (Adamowicz et al., 1994;Hensher, 1994;Schipper, 2010).
A consistent form of analysis was applied to all three case studies: Companies Alpha, Beta and Gamma. These were composed of one private firm and two public firms. We found that the private firm (Company Alpha) had faced free choices for both consolidated accounts and individual accounts. By contrast, the two public firms (Companies Beta and Gamma) were found to have 'tied' choices for consolidated accounts but were at liberty to choose their accounting modes for individual accounts. the sequential decision-making process (Birnbaum, 2010;Colman & Stirk, 1999 Confronted with free accounting choices, Company Beta and Company Gamma applied the nested decision-making process (Hensher, 1994;Tu & Goldfinch, 1996). Company Beta aimed to take all key aspects into account when making decisions. The nested decision-making process helped Company Beta to have a better outcome for the whole organization. For Company Gamma, there was no large difference (e.g. in techniques) across different regimes.
Hence, it was unnecessary for the firm to examine accounting modes in detail or in stages: It was easier to make decisions simultaneously.
Our empirical analysis shows that Companies Gamma and Beta did not perceive clear distinctions between the significance of regime choices and of technique choices. This is probably the reason why they adopted the nested decision-making process, rather than the sequential process of Lex or CoLex.
When companies make decisions by using un-staged processes (viz. Nest), they consider regime choices and technique choices at the same time. They will choose that financial reporting form which leads to the best result for them (i.e. the maximum utility) when various crucial aspects have been considered, including regimes and techniques.
Their utility functions can be expressed as u(X ij ) = f(x i , x ij ), whose form is associated with companies' priorities in financial reporting (e.g. the relative importance of regime and technique choices). As mentioned by the interviewee of Company Beta, it is companies' goals that will determine whether the nested and the sequential decision-making processes can result in the same accounting pattern.
Comparing Company Beta and Company Gamma, they both had tied choices when preparing financial reports for consolidated accounts. As public firms, they could only use IFRS as the regime for consolidated accounts. Thus, compulsory IFRS adoption forced public companies to elect the regime before they could choose techniques.
In a sense, they applied the staged decision-making process involun- The results reported here also show that firms adopted different decision styles in evaluating accounting modes. For instance, Companies Alpha and Gamma both tended to decide upon financial reporting modes subjectively, because they sought ease of execution. In contrast, Company Beta preferred to decide between accounting alternatives with the help of more tangible evidence (cf. Bruns, 1968;O'Reilly, 1983). Company Gamma also used numerical data and scenario analysis, as necessary, to help its decision-making. It should be noted that both Companies Beta and Gamma applied the nested decision-making process when confronted with free accounting choices. In the nested case, when companies make decisions simultaneously, they need to consider all key aspects at the same time. In this situation, supporting data (e.g. by scenario analysis) can be very helpful (March, 1987). Therefore, it is no surprise that both Companies Beta and Gamma liked to have such supportive data when making reporting decisions, even if this requires using more resources.